I know in the past there have been some weird issues with triple repetition but I think if you click the offer-draw before making your move and then make the move creating the triple-repetition, then it should allow the draw (assuming it truly is correct). I haven't had that happen in a game here and haven't seen if it has been tested more recently to verify how it works in practice.
They system should never automatically award the draw in such situations and really shouldn't even notify the player that that situation exists. In an OTB game, the player has to be aware of the repetition (or 50 moves condition) and accurately claim it. Same should be true here as long as the implementation of the claiming works (preferably with the click draw before move option and a check after the move or with a claim after the move).
This was a game I played when I first started playing on here. The game ended in a draw though it will proclaim that black won even though this is not the case. Prior to coming to this website, I was unfamiliar with the draw feature and I will explain after posting the game why the internet should not even attempt to produce a "claim draw" feature or should mark this better. Most of the places I have played on in the past immediately end the game at three-fold repetition and the game ends in a draw. Note that three-fold repetition is third position repetition and not necessarily repeated moves.
The game in question is here:
As we can see, there is a significant problem--chess.com DOES NOT follow FIDE rules to the point! If it did, a draw has to be claimed not immediately following the person's move but PRIOR to them making the move that results in three-fold repetition. Therefore, IF chess.com WANTS to follow FIDE rules, it needs to change its draw feature on this website to enforce draws when the player simply has an intention to mark a three-fold repetition. However, chess.com for some reason also takes away your ability to claim a draw after the following move in accordance with FIDE rules. BUT as I have already pointed out, it does not follow FIDE rules to the point so why is there a need to follow FIDE rules on this? Further, as the three-fold repetition merely is the position, then there should at least be a flashing light on the draw button at this point in order to help beginners know that this point is a draw. I shudder to think how many people have lost games because their opponent has been able to make his move breaking the three-fold repetition prior to them being able to claim a draw. As chess.com does not allow you to claim a draw prior (which is something that FIDE enforces) and takes away your draw privilege immediately after your opponent has completed his move (which is something FIDE would not allow as you need to claim the draw prior to making your move by writing your move down on your score sheet and showing it to the arbiter), I see no reason why chess.com needs to be a stickler on the rule that a draw can only be claimed immediately after the third position or 50 move rule is breached.