There can be reasonable disagreement on how the specific phraseology ("cross [FIX] at 250 knots") in the question should be interpreted with respect to what speed the pilot is or is not obligated to maintain after crossing the [FIX].
in my opinion, in the U.S., you would cross the [FIX] at 250 kts as per the controller's instruction, and then, in the absence of any other instructions (including flying a STAR/SID or another procedure containing published speed restrictions), you could fly the speed of your choice (of course adhering to any regulatory speed restrictions).
I cannot find any specific published procedural guidance/requirement (e.g. Aeronautical Information Manual-AIM, Air Traffic Control handbook-JO 7110.65, regulation, etc.) that specifies that a pilot must maintain 250 kts once crossing [FIX] (based on the ATC example phraseology given in the OP's question) until receiving a new clearance/instruction (such as a different speed assignment, clearance for an approach, etc.)
Although most pilots would likely maintain 250 kts as long as they could, I can't find any published requirement obligating them to do so (based on the ATC phraseology example given in the OP's question).
If ATC wanted the pilot to maintain 250 kts after crossing [FIX] I believe the instruction should be (something like) "Cross [FIX] at and maintain 250 knots."