Your routine was anchored to a day you're about to leave behind.
Travel breaks medicine routines for a structural reason: the anchors disappear. Breakfast happens at a different hour, bedtime moves, and the visual cue of the pack on the kitchen counter is two thousand miles away.
Most of the fix happens before you leave, and the time-zone question specifically is one to settle with a pharmacist rather than work out on the plane - because the answer differs a great deal between medicines.
There is no single right answer, which is exactly why it's worth asking. For some medicines the sensible approach is to shift gradually toward local time; for others, staying on home time for the trip is simpler; for a few, the interval between doses genuinely matters and needs planning.
Write the plan down before you fly, with both the home time and the local time for each dose. Doing that arithmetic jet-lagged, on the second morning, is where mistakes happen.
Since the visual and routine cues are gone, travel is the situation where a reminder earns its place most clearly. Set it to local time once you land and decide, in advance, which meal or moment each dose now attaches to.
If you're travelling with someone, tell them what you take and where it is. That matters more abroad than at home.
Worth saying plainly, because the wrong tool applied to the wrong problem wastes weeks:
Ask your pharmacist before you travel - the right approach depends on the medicine, and for some the interval between doses matters more than the clock time.
Yes, in original labelled packaging, with enough spare for delays. Hold luggage can be lost or delayed and replacing a prescription abroad is slow.
For some destinations and some medicines, yes - particularly controlled ones or injectables. Check the destination's rules well in advance.
Getting a prescription abroad is possible but slow and sometimes expensive. Take extra; it's the cheapest insurance available.
Reminders arrive on WhatsApp wherever you have a connection, at the times you set - useful precisely when the usual cues are gone.