Tricky situation although its very simple

Player A declares an attack with his monster on B player's atk position monster. Player B answers with a Mystical Space Typhoon as a chain trying to destroy one of A player's facedown cards. Then Player B chains Book of Moon to it trying to flip A player's monster facedown. Then A player responds to it by chaining Dimensional Prison trying to remove attacking monster from game.

People say to this: You cannot chain Dimensional Prison as it will miss the timing of its activation. (They refer to that the time of activation of Dimensional Prison is not at "Declaration of attack")

Now let me explain this.

Battle Step

In the Battle Step of the Battle Phase, the Turn Player selects, and announces 1 monster he/she wishes to attack with, and either targets 1 of the opponent's monsters he/she wishes to attack, or, if he/she is able to, announces that he/she wishes to attack the opponent's Life Points directly.

When an attack is declared, the Turn Player retains Priority to activate effects. At this time he/she is free to activate cards that perform an action when a monster attacks or any other effect with timing he/she can meet.

If the Turn Player decides that he/she will pass, the opponent is given a chance to activate effects that respond to the attack ("Sakuretsu Armor", "Mirror Force", etc.) or any other effects with timing he/she can meet.

If the Turn Player passes, and the opponent passes as well, the chance to activate cards like "Sakuretsu Armor", "Mirror Force", "Magic Cylinder", etc. is GONE.

Now let us see facts about chains. It is possible to chain when a monster declares an attack. The time holds on at the point where first chain occurred. Every chain link to that will not move time from that point. It will still be same timing of Battle Phase no matter how many chains were linked to it. This means if Dimensional Prison was chained at this point but as chain link 3, the time is still at that point, the point where declaration of attack occurred. Thus, timing of Dimensional Prison will be correct and there should be no problems to activate it.

People confuse this situation with this one:

The Turn Player declares an attack with a monster and passes priority. The opponent responds with his Set "Sakuretsu Armor". The Turn Player then Chains "Trap Jammer". Neither player has a response, so "Trap Jammer" negates and destroys "Sakuretsu Armor".

The opponent then wants to activate "Book of Moon", and he/she can, because "Book of Moon" does not have to respond to an attack in order to be activated. The initial response window has passed, but since the Turn Player cannot enter the Damage Step until both players agree to do so, other cards may still be activated. A Chain with Dimensional Prison to Book of Moon here is not possible since response window to an attack has already passed.

Correct me if I'm wrong.

Then, What should I do if you're not wrong? since you are not.

To put it simply, activating something doesn't move the "Last-thing-to-happen" event.
However, when a chain resolve, the gamestate move the "last-thing-to-happen" to that resolution.

you wouldn't say, when you summon JD and activate it's effect, your opponent missing the timing to activate BTH are you?

And, just something I'd like to inform.
Both player(starting from the turn player per usual) have priority to activate a trigger effect that respond to an attack(i.e. battle fader)before the turn-player is allowed to activate spell speed 2 or higher. Since if it doesn't, battle fader can't be activated due to inferiority of spell-speed.

I just wanted a confirmation so that some people question their knowledge about these things.

Confirming. If a Counter trap negates a trap such as Dimensional Prison, you can still activate Spell Speed 2 cards before Damage Step, but ONLY if they do not have attacking as an activation requirement. Book, Waboku, Compulsory, all these cards do not have a monster attacking as their activation condition. Therefore, you can start a new chain with these cards, before Damage Step, after the Prison/Jammer chain resolves.