Hola Emanuel
You may hear casi with the same meaning of "nearly" used with the past tense. If it is a phrase used in that specific "anecdotic" context, I mean, with an element of surprise and also colloquially speaking, the present tense is the most natural tense to use even when it's an action that has already passed. It's also to do with the historic present, to give a bit of drama to the action and make it more real when telling it.
If you use it in a sentence where the action is seen as incomplete, you then find a past tense.
See this example:
El bebé se puso de pie y casi andaba, pero todavía le faltaban unas semanas para caminar correctamente.
The baby stood up and he was nearly walking, but he still needed a few weeks to walk properly.
Here, you can see how that action of walking was an action that we don't see as complete, hence the use of a past tense, and of course the imperfect to be more descriptive.
I hope this clarified it.
Saludos
