The process is such that the IEEPA refunds will proceed with the liquidation of the imports.
Customs basically finally closes a file (liquidates) about 315d after the entry. So if something was imported on July 1 2025, then May 12 2026 it would liquidate.
Importers having filed their CAPE data (which was super easy, took me about 15 mins for more than 1200 entries), those entries will be flagged for the return of the IEEPA duties plus interest, which is a usual customs thing.
Note that 'issuing the refund' and getting the refund $ actually might take a bit. Some brokers are suggesting it might take up to 60d for the funds to flow, or, it could just be CBP is awaiting June1, as the White House still has a chance to protest the CITA court ruling until then. (There is no suggestion they will but still, better to wait then have to un-de-retro-re-bill people for refunds that need to come back or whatever.)
Short version, it's not like these companies will suddenly get a giant pile of refunds; they will trickle back at (approximately) the frequency they went out last year.