While playing MTG, who is responsible for a triggered ability and what is the limit in time to claim it?

Let put an example:

Using the activated ability of Obsidian Fireheart, I add a counter on one of my oponent's lands. Then I end my turn and he starts untapping his cards.

Is it my responsibility to tell him "hey!, don't forget to lose your 1 life" and can he intentionally foreget it otherwise?

Also, if it's my responsibility to tell him, what is my limit in time to do so?

While playing MTG, who is responsible for a triggered ability and what is the limit in time to claim it?

Let put an example:

Using the activated ability of Obsidian Fireheart, I add a counter on one of my oponent's lands. Then I end my turn and they start untapping their cards.

Is it my responsibility to tell them "hey!, don't forget to lose your 1 life" and can they intentionally foreget it otherwise?

Also, if it's my responsibility to tell them, what is my limit in time to do so?

While playing MTG, who is responsible for a triggered ability and what is the limit in time to claim it?

Let put an example:

Using the activated ability of Obsidian Fireheart, I add a counter on one of my oponent's lands. Then I end my turn and he starts untapping his cards.

Is it my responsibility to tell him "hey!, don't forget to lose your 1 life" and can he intentionally foreget it otherwise?

Also, if it's my responsibility to tell him, what is my limit in time to do so?

While playing MTG, who is responsible for a triggered ability and what is the limit in time to claim it?

Let put an example:

Using the activated ability of Obsidian Fireheart, I add a counter on one of my oponent's lands. Then I end my turn and he starts untapping his cards.

Is it my responsibility to tell him "hey!, don't forget to lose your 1 life" and can he intentionally foreget it otherwise?

Also, if it's my responsibility to tell him, what is my limit in time to do so?