Oathbringer clarifies the exact mechanics in "Alone Togther", Rlain's chapter
Soon after he left through the Oathgate, everyone would slowly start to lose their powers. They'd be gone in an hour or two. Kaladin had to be relatively near-Sigzil had placed their maximum distance from him at around fifty miles, though their abilities started to fade somewhere around thirty miles.
Kaladin travelled to Urithiru significantly later than Shallan did. Until then, he was fighting above the Shattered Plains, presumably within fifty miles of the warcamps
The Shattered Plains had become shattered again
Kaladin strolled across them with Szeth's Shardblade on his shoulder. He passed heaps of rocks and fresh cracks in the ground. Enormous puddles like smalll lakes shimmered amid chunks of broken stone...
He summoned Syl as a Blade, following Sigzil's instructions, and used her as a key to work the fabrial.
Kaladin then has a short conversation with Dalinar:
One of the pillarlike plateaus nearby flashed... Someone had opened the Oathgate. Dalinar stepped up beside [Shallan] and they waited tensely, until a group of figures in blue appeared at the plateau edge and started down the steps. Bridge Four...
"There was an assassination attempt," Kaladin said. "I stopped it, but the king was wounded. I put him someplace safe before coming to help Dalinar."
Then the scene transitions to Lopen, where he displays his newfound abilities. Assuming everything is chronological, there is only a small time gap between Kaladin using the Oathgate and Lopen discovering he is a squire.