YOu are correct, and no one said you broke any rules. I was saying you qualified for something because of a rule.
This is how you get Menagerie.
You said it yourself, your board consisted of 4 beasts, 1 dragon, and 1 pirate.
You only need 3 different types to qualify.
That would be how you would avoid being considered “in” more than just 1 tribe. For example if you had 2 of X and 2 of Y tribe you’d be in both X and Y tribes for your timewarped options. In order to avoid this you then focus on making sure you are “in” the tribe you wish your options to be by eliminating one minion or buying another that shifts that balance. Hence the 2 of X tribe and no more than 1 of any other tribe rule you are mentioning.
But this doesnt mean you can avoid menagerie because all it takes at all is 3 different tribes on your board at all. you could have 4 mechs, a beast, and a demon. and you would not be considered only “in” mech you would be considered “in” menagerie as well as Mech. The two rules are not exclusive, they are allowed and often do, overlap.