IB stop order trigger methods

[braincell]

I'm working on my backtester and I'd like to be sure I'm simulating stop triggers with full accuracy, using Interactive Brokers. I think I know what each of the trigger methods is supposed to do, but I'm seeing slight differences compared to the last/bid/ask in my feed vs when they really get triggered.

This is how I assume they work for Buy Stop:

-Double bid/ask : send market order if there are two consecutive ask (for buy) quotes AT or ABOVE the stop price

-Last : send market order if the last price is AT or ABOVE the stop price

-Double Last : send market if two trades happen AT or ABOVE the stop price

-Bid/Ask : send market order if there is one Ask quote AT or ABOVE the stop price

-Last or Bid/Ask : send market order if Last or Ask reaches AT or ABOVE my buy stop price

-Mid-Point : send market order if the mid-point is AT or ABOVE my buy stop price.

My main question is:
Am I right in assuming "AT or ABOVE" or is it only "ABOVE" (for buy stop in my example)?

I found a further confusing explanation from IB's website, for example:

Bid/Ask - For a buy order, a single occurrence of the bid price must be at or above the trigger price. For a sell order, a single occurrence of the ask price must at or below the trigger price.

Meaning a buy stop would be triggered if the BID is at or above stop price, meaning when it converts to a market order, the ASK (at which you will then be buying) could have run away significantly. This makes even less sense!

So if anyone with direct experience on this (or even better someone from IB) can give me their opinions, that'd be great.