Can the reaction effect be triggered multiple times or one time only? I thought the reading of the card was pretty clear but I was recently over-ruled by 6 players at my local tournament and decided to get clarification.

I read the card as each time I win a conflict at the province and claim the ring I get to resolve it, and this triggers each time I win the conflict at this province. For example I win a military Air conflict at the province as defender and resolve the air ring. Then in their next attacking conflict they declare political earth and I win I should be able to resolve the earth ring. (Or if this is an attack in a different phase, it shouldn't matter and should trigger each time.

I was told the effect can only be triggered on one conflict and does not resolve again in any conflicts afterwards. I believe they have this confused with "on revealed" and "on break" reactions that other provinces have. Ultimately this had no effect on the outcome of the game, but I am looking for clarification in future games if I want to continue running this province.

Thanks in advance.

Actions on cards by default are once per turn. They will say otherwise if not (See intimidating hida for an example of one that you can use twice a turn). This applies to all cards.

However, you can reuse it once per turn on other turns once its been revealed.

This reaction is an activated card ability, so it's once per turn by default (until written otherwise, like watch commander's unlimited reaction).