I disagree, it's still law, civil or criminal. The point of the analogy is just that if you commit offences and get punished for those offences, you can't commit more offences later with immunity. The FA seem to be looking into this to see if there are any new offences that haven't been covered.
The example you give of being on remand/time already served - that's missing my point IMO: You seem to be making an argument about appropriate sentencing for an offence, & I don't disagree with it, but my point was that if there's then a new offence it still needs to be looked into.
So in your example, your fella on remand doesn't get a free shot to commit more crimes later just because he's already getting punished for the first ones.
Here there's been an investigation into specific betting offences.
There has been punishment given for those specific betting offences.
If there are then more betting offences committed afterwards that weren't dealt with by that investigation and punishment, you can't just ignore them because he's already been punished for previous similar offences. That's what I'm saying.
So I don't think the FA can do him for the things he's already been punished for [i.e double jeopardy]. But if he has potentially committed new offences outside the scope of his current ban then they have to be looked into.
Also I'm not saying his ban should necessarily be increased. As I said: "If there are more offences though it could be that punishments already imposed are taken into account when deciding what new punishment is appropriate."
If there are more offences & the FA charge him, they absolutely might take the current punishment into account. Eg. they could punish him with a fine & suspended ban. But that's a sentencing issue based on the facts of the case, you need to go through the proper process to get to that point.
Imagine if the FA does investigate and it turns out he bet on Milan to beat us in the Champions League...