This happened at a recent FNM and while I think I know the correct rulings I'd just like to get clarity on this as the situation did cause more issue than it should have (and also because every man and his dog is playing UR Delver in Modern these days).

Situation 1: Active player has a Young Pyromancer in play and casts Treasure Cruise draws three cards, plays a land for the turn and then passes the turn. He then looks at the board and goes “oh, and I get a token from the Young Pyromancer”. Opponent says he missed the trigger and is not allowed the token, Player then asks for a judge opinion.

My ruling:

Since it is not an optional ability, put the ability on the stack and Active player gets a 1/1 token.

Situation 2: Active player has an unflipped Delver of Secrets in play, during the upkeep player reveals the top card for the Dlever trigger and calls it out by name "Combust". Player then draws the card and clearly starts thinking about his play, when he looks down he sees that the Delver is unflipped and goes to flip it over. Opponent says that the player has missed his trigger and cannot flip it. Judge is called.

My ruling:

The player acknowledged the Delver trigger and revealed the card. The optional part of the trigger is the reveal and this had happened, so nothing was missed. Since the card was revealed - the trigger was not missed, Delver was supposed to flip and the player must just update the boardstate to match the gamestate.

For the first situation, the JAR asks us to use our judgement to decide whether to put the trigger on the stack. If not much has happened, then put it on the stack. If lots of decisions have been made then don't. And for the areas in between, use judgement. From your description, not much has happened so I'd be fine putting it on the stack and giving him the token.

For the second situation you're spot on - I'd do exactly the same.

In both situations I'll explain why. In the second situation, if I get the impression that the opponent was trying to be a rules lawyer to screw his opponent out of something I'd caution him about his approach to Regular REL events ;) But if it's just a genuine misunderstanding of how Delver works then I won't mention anything. At events like FNM it's important not just to answer rules questions and fix errors, but to also try and maintain a fun and welcoming atmosphere. And if someone is being overly rulesy, have a polite word.