I'm not sure whether I'm using the word manifest correctly. For example, today at work my work mate said he only sees me when it's getting busy and I said jokingly:
I just manifest when you need me.
Is this wrong?
Strictly speaking, 'manifest' (verb, no object) meaning 'appear' is used about ghosts or spirits, but would be understood if used in a jocular sense about a person, especially if humorously likening them to a spirit, demon, etc.
Yes, if you're a ghost or a spirit. According to Oxford Dictionary:
(no object) (of a ghost or spirit) appear.
Example: one deity manifested in the form of a bird
Otherwise, manifest should only be used as a verb when you want to, according to Merriam-Webster:
(to) make evident or certain by showing or displaying
manifest, in this sense, is often used to refer to abstract concepts or emotions rather than actual, tangible objects. Example:
Her behavior problems began manifesting themselves soon after she left home.
clearly revealed to the mind or the senses or judgment; Choose the verb manifest when someone shows something for everyone to notice.
As in your sentence with a slight modification, the usage is correct in AmE:
I just manifest myself when you need me.
There are other senses of 'to manifest', ghostly is but one. OED