I just realised that when Claire went to the lab on her last day alive in the past, she was wearing green pants and a white lab coat. This must mean that the outfit she wears during the present-day events of Lost Future must have been acquired after she arrived in the future.
Dimitri was the first on the scene after the explosion, so he found Claire’s body amid the rubble wearing these clothes she’d changed into in the future, an image which he likely carried with him for the rest of his life. This means he probably recognised the outfit when Claire first put it on, 10 years later.
Can you imagine Dimitri’s growing unease as Claire (or “Celeste”) slowly accumulates more pieces of clothing during her stay, a blue jacket here, a yellow scarf there, and he’s not sure why he’s uncomfortable when she wears them, until one day when she combines them in a particular way and suddenly it clicks and he realises that he doesn’t like them because he’s seen them on her before.