how would you regard this situation

thanks for the annotation !

so mate in 1 doesn't necessarily means mate in 1 move ?

if the analysis says M1, its 1 move.  

If it says M10, the opponent can still make a mistake to cut that down to M1 or M3 or whatever.  If you make a mistake, you can change M10 to no mate anymore, or M10 again, or M25, or whatever... you have to follow the optimal sequence to get the mate, but the computer only lists FORCED move mates, and if the forcing side makes a poor choice or if the defending side has a choice that makes it worse than it was (shorter sequence) you don't get that shorter number as it assumes best play both sides.   I almost always take longer than optimal to mate, as I am on the clock and looking to avoid a draw, so I will be more careful than if  I had all day to study the shortest paths. 

A mate in 1 definitely means mate in 1 move. The mate in 1 error wasn't for your move though, it was for the opposing move that came right after. Your opponent blundered mate in 1, which you took.

well, okay, why then did it put the 'missed win' on my side ? i wonder

Missed wins aren't necessarily mate in 1s, but as I mentioned when going over it earlier, you missed a forced win, a mate in 4. The only reason you got checkmate next move was your opponent's blunder.

got it, also got now what jonnin said, alright, cool...