Not necessarily. They may have identified all the serial numbers of terminals legitimately used by Ukraine then simply blocked all terminals not on that list.
Crimea is geofenced. That's why Ukraine officials contacted Elon and asked him to enable it so that their drone boats could attack Russian navy there which Elon refused to do. It's literally illegal due to US sanctions to Russia. This is what the author Walter Isaacson wrote about in his book but for some reason spun it around claiming Elon disabled it to prevent the attack when in fact it wasn't enabled in the first place. He has later issued a correction stating that what he originally said was incorrect but this is conveniently ignored by pretty much everyone and when ever I point it out I get downvoted.
To clarify on the Starlink issue: the Ukrainians THOUGHT coverage was enabled all the way to Crimea, but it was not. They asked Musk to enable it for their drone sub attack on the Russian fleet. Musk did not enable it, because he thought, probably correctly, that would cause a major war.
And before someone comments on the "major war" point, those are Walter's words, not Musk's. Elon said that agreeing to do so would "make SpaceX explicitly complicit in a major act of war and conflict escalation" but also later added that had he been contacted by the White House and asked to enable it he would have but they didn't.
SpaceX has to do the disabling, so they are on board. I like to imagine that this was one of the conditions for the multi-billion dollar purchase of Starshield, along with exclusive use and SpaceX not being allowed to disable it anywhere for any reason.