Sankashti chaturthi is decided by moonrise

The chaturthi that is running at moonrise takes the day — not the one running at sunrise.

Almost everything in a panchangam is decided at sunrise. Sankashti is not, and that single fact explains most of the confusion around its date.

The rule

The tithi covering moonrise decides the day. The text states it plainly in the second pariccheda, referring back to the general rule of the first.

Because the fast is broken after sighting the Moon, the observance is tied to moonrise, and so is the day it falls on. It would be strange for the rule to be otherwise.

Why the date can look wrong

Moonrise on a krishna-paksha chaturthi is late — typically well after 8 pm, and it drifts by roughly fifty minutes a day. So a chaturthi that begins in the afternoon and ends before the following night's moonrise can be the chaturthi at sunrise on one date while the chaturthi at moonrise belongs to another.

Compare a sankashti date against a plain chaturthi listing and they will sometimes differ. They are answering different questions.

What this means for a place

Moonrise is local. Two towns far enough apart can see the Moon rise on opposite sides of a tithi boundary, and on those rare nights their sankashti falls on different dates. Any listing that does not name a town has quietly picked one for you.