Yes indeedy. Time is time is time and when, in each half, 45 minutes plus however much injury time is added on has expired, it is OVER. Blow the whistle. Once it has blown there is no going back.
Whay most refs do in reality is, at the appointed second, when a team is attacking, let them "finish" the attack and then blow for time. The second a defender gets the ball, the attack has broken down...... it avoids argument, especially at the lower levels where they have no idea that they are even in injury time......
I fell foul of a parent at U9 level many years ago. His lad's team were losing a hell of a lot to only 1 or 2. They attacked from their own goal and had reached halfway, time was up, I blew. Dad was livid. They might have scored..... you're ruining their enjoyment, another goal would have been good for morale.....
I told him that I merely applied the rules but with some bending. Doing that rather than make allowances for "their age" etc prevented them from misconceptions and clashes with refs in later life. I pointed out what I did at throw ins. At their age, many throws are foul throws. I stopped play (the Dad would rather that I had let play carry on), told the offender what he had done wrong, showed him the right way and then let him retake the throw (as opposed to giving the throw directly to tthe opposition) with the warning that the next one, and as I had also given the coaching to the rest of the players on both sides, would be penalised.
A lot of the problems refs have with amateur players at the lower levels is that the players, most of them anyway, do not know the Laws........ no wonder they think you are crap. I have even had Captains win the toss and say "we will kick off", get most uppity when told "no you won't, you will choose which goal you wish to defend in the 1st half".