I'm trying to utilize a rewirte rule inshtaccss then when a person makes its way into "/page/my-title", it'll direct him to "file.php?title=my-title"

I personally use the next:

RewriteRule ^page/?$ file.php?name=1 [NC,L]

However, it redirects me only if Time passes to "/page" and never when i am likely to "/page/my-title".

Your rule includes the $ anchor, meaning the request string needs to finish there. That's not really what you would like, since you need to capture anything following the / and employ it inside your substitution.

Possibly try something similar to this?

RewriteRule ^page/(.*) file.php?name=$1 [NC,L]

Also, note, you'd =1 inside your question, rather than =$1.