2it does nothing by itself
The bottle only matters when a dye sits in the matching slot. Then your minions take that color instead of their default. It cannot be reforged, so putting it in a normal accessory slot wastes a slot you could be using for stats. It belongs in a social slot, permanently.
what stays the wrong color
Sentries ignore it, and there is no other way to color them either, so a build leaning on turrets gets nothing here. The Forbidden Sign and the Stardust Guardian also skip it, but those two follow whatever dye is in the pet slot, so they are recoverable. Team Dye is the one dye that will not carry over to minions at all.
when you can buy it
The Zoologist only lists it once your bestiary is filled out well past the point of casual play, which puts it firmly in the back half of a run. It is a reward for having caught and killed a lot of things, not something you can plan a summoner outfit around early.