Minor skill pts are not retained this way. You could blast away and level up a minor skill to 100 in a single level if you wanted to do so.
There is extensive information about this process on UESP wiki. If it doesn't make sense, just play the game with several different builds and track how the skills and stats development occurs. You may need to see it in action. It's much easier than how it may sound in all these descriptions.
In any event, note the math (again). Skills will always start at a minimum of 5 pts, and they have a max of 100. Major skills start at a minimum of 25. There are 3 skills per attribute (excluding Luck, of course). Therefore, for any non-Luck attribute, you can easily calculate how many pts you need to get it to 100.
For example, let's look at a hypothetical build where the three Intelligence skills start at 25, 5, and 5 (I don't care which ones are which and this hypothetical build would probably have at least a boost of 5 or 10 pts on one or more skills due to race and birthsign, but this is just to illustrate the math). 25+5+5 = 35 pts, right? Max of 100 in 3 skills would be 300 pts total available pts for leveling, except that we don't start at zero, of course, so we have to adjust our max available pts accordingly. 300-35 (from the actual starting value of the 3 skills) = 165 pts max available. The question now is ... what does the Intelligence of this build actually start at? I don't know since it depends on race, but let's just say that it starts at 40. That would mean it would need 60 more pts for 100 (maxed). At 5 pts per level up, that would require 12 levels at a minimum of 10 pts per level (for the +5 on Intelligence), or 120 pts total in order to maximize Intelligence at 100 (eventually). We already calculated that we actually have a total of 165 pts available, so this means that there are an extra 45 pts that can be "wasted" as we go through our progression and seek 100 Intelligence. You could burn those points on a minor skill right at the beginning in a single level and take one of the 5 pt minor skills to 50 within that one level, or you could spend the 45 pts at your leisure over a period of several levels, even waiting until after getting Intelligence maxed at 100.
You can do the same type of calculation for each attribute and its associated three skills, of course.
This is where the real strategy lies for maxing characters. As noted previously, some skills are much easier to control and develop than others. The three skills for Intelligence are all very very easy to control and develop, for example. Therefore, even if a character starts with low intelligence and low values for the three governed skills, it's very easy to develop those skills (and add +5 modifiers to intelligence at level up) compared to pretty much any other attribute and associated skill set (i.e., all the other stats have one or more skills that are at least a bit more difficult to develop and control than the three intelligence skills). Willpower would probably be the second easiest (the magic schools are the easiest to develop and control of any of the various skills, and that's why Intelligence and Willpower are almost certainly the easiest stats to develop and control).
In other words... you will always have some pts you can waste in each set of three skills. You can save them and waste them later, or do it early on in the character's life. Obviously (I think) max difficulty encourages you to waste the extra pts early so as to develop a stronger character at the first couple of levels (and avoid dying due to sheer weakness of skills). Perhaps one good example of the issue would be your basic Flare spell. 6 pts of Fire dmg... except max difficulty changes that to 1 pt. Umm... 1 pt of dmg isn't going to do much against an awful lot of enemies, even at low level. Some enemies (Trolls, for example) just regenerate the dmg, so you effectively do zero dmg to them with this spell on max difficulty. That's not true on normal or lower difficulty so it isn't an issue, but max difficulty will require you to revise your approach if you relied on blasting things with Flare previously.