A possible airspace incursion event when coordination regarding activation of a restricted area was not timely.

Narrative

I was conducting RADAR OJTI. W174 and W465 had been active all day. Aircraft X was climbing Southwest bound with crossing traffic. We were advised that W465 was no longer active. When the status board was updated; I observed W174c was not being shown active. I questioned this and it was confirmed that it was cold. With this information separation techniques were discussed with my trainee that would allow Aircraft X to safely climb above traffic. It was decided to place Aircraft X on a heading that would remain clear of traffic. This became possible with W174c being inactive as the vector would put the aircraft in the warning area. When vertical separation was established; Aircraft X was cleared on course. We were offered a break and during the relief briefing it was stated W174c was cold. The D-Side heard this and stated it was going active. The time of activation was questioned and it was very close to the current time. Aircraft X was issued a vector to expedite clearing the area and the D-Side called the MRU to cap the airspace below Aircraft X. I believe this was done timely but I am not positive. Recommend ZMA have procedures in place for SUA activation. When correctly followed this should be sufficient.