I had a look at the manual, and there is quite a lot of more or less wrong, or at least misleading information in there, especially around the biology. I am a virologist by training, but have had a fairly varied career, including being involved in teaching of food microbiology - such as yogurt making, so have some experience in this area. I've also been making my own yogurt at home for more than 10 years using the EasiYo Maker system (there's one on the link I have put in the next paragraph).
Also note, they are a company, which sells, among other things yogurt sachets for making your own yogurt; they are trying to sell you these products!
Many companies make yogurts and similar products with particular strains of the bacterial species, however, in general, unless they have done some extensive optimization and/or selection, they will be using a regular species and probably from a common strain. When they do have something special, they typically ensure that you know it in terms of advertising and price. Have a look at "Yakult", which widely vaunts its "Shirota" strain
The probiotics in yogurt are generally bacteria of the genera Lactobacillus (particularly L. acidophilus and L. casei (now called Lacticaseibacillus casei)) and Bifidobacterium (often B. bifidum). These are anaerobic bacteria, meaning they don't grow or don't grow well in the presence of oxygen, that make up a major part of the bacteria in our intestines. The genera are both very diverse having lots of different species and have genomes that are quite malleable - in that they can acquire or lose genetic components depending on the environment and as such can be difficult to maintain in anything other than the proper conditions. Commercial vendors get around the problem of change of characteristics by having validated stocks that are assessed for the characteristics that are wanted, grown in bulk, frozen down (often at -80 C/-112 F) in small aliquots and then used for inoculating the product. Loss of genetic characteristics is entirely possible, but unlikely - in my experience you are more likely to get additional characteristics. We tend to get a mucilage producing variant over time in plain yogurt. No change in flavour or anything else, just a genetic characteristic that turns up, especially so if we use vanilla for flavouring.
Now - on to your manual. I can see some problems with how it works that makes me think that the largest problems you will have are contamination issues - yeast and normal gut microflora from you or a pet will grow very happily in warm milk. The aim of adding 125 ml of inoculum (starter) to your milk is to overcome this problem to some extent by having a lot of the wanted bacteria from the yogurt in there, using up available resources and turning the milk sour (relatively) rapidly. Contaminants, which usually are added in small amounts accidentally, will get out competed by the good ones and the acidification will create a non-optimal growth environment for the contaminants. The boiling the milk beforehand is also to lower contamination chances.
You can, of course, get away with much less inoculum - we use about 15 ml (1 tablespoon) in our litre (~2 pints) yogurt. However, to do this, you should take this from the yogurt immediately after it has been cultured into a very clean sealable container, and put it into the freezer (-20 C/-4 F), where it will keep reasonably well for a couple of months until all the bacteria die off from ice crystal formation. The risk you run with the smaller inoculum is that it takes a bit longer to get going. A typical biological system, such as in culturing yogurt, has 3 phases of growth - lag, logistic and plateau (S-curve). The lag is at the start when there is slow growth until the inoculated bacteria create a favourable environment for growth (in this case acidic) and reach a point where they start to divide/replicate logistically, replicating about once every 20-30 min. Once the population reaches a point where most of the resources (in this case nutrients from milk) in the environment are used up, the replication slows and reaches plateau. The smaller the inoculum, the longer the lag phase will be - which gives more time for contaminants to grow.
For the inoculum do NOT use yogurt that has been sitting in the fridge until almost used up and you need to make some more. The reasoning here is that this is more likely to have contaminants in it; the more times the container has been opened and things put in it (e.g. spoons), the more likely contaminants have been introduced. I suspect this is the real reason they say not to use it more than 3-4 times.
If you get a packet mix of yogurt - the first thing you should notice is that it is dry - all it is, is a mix of bacteria and milk-powder and maybe flavourings and colourants. You can replicate this at home with ordinary milk powder and some inoculum. Just follow the instructions on the milk powder packet to get your required milk volume, and add your frozen inoculum and mix. You can also portion the packets out and make up the bulk with milk or milk-powder. Ours is usually done within 6 h of incubation. Longer gives more acidity (e.g. Greek-style) and firmer yogurts, while shorter is sweeter and more runny.
If you notice a non-yogurt smell in your yogurt, or notice changes in texture (no change in recipe) or flavour, then you should throw out your inoculum and get some fresh from a packet or store-bought live culture yogurt.