This is an English question, not a Spanish question. Most people who use this phrase in English do not in fact know any Spanish at all, just as those who use Bon voyage! or Bon appétit! may well know no French to speak of.

English speakers, particularly in America, not uncommonly use the phrase hasta luego borrowed from Spanish in their English-language speech as a way of saying See ya!

The Spanish preposition hasta corresponds to English until, till. There are lots of versions of these various hasta X phrases floating around, the most common probably being ones like these:

Hasta la vista
Close to French au revoir, so in Spanish essentially (not literally) “till we see each other again” but not quite so formally; more like “see ya later” or “be seein’ ya” perhaps.
Hasta luego
Literally “till then” in the original Spanish.
Hasta mañana
Literally “till tomorrow” in the original Spanish.
Hasta la mañana
Literally “till morning” in the original Spanish.
Hasta después
Literally “till later” or perhaps “till afterwards” in the original Spanish.

Your phrase, hasta luego, is a very general thing which is heard all the time here in the southwest United States. It just means “until whenever”; it is not as long-term as hasta la vista.

All are rather casual, and you should not expect listeners to use them per their exact original senses from Spanish. This frequently occurs with loanwords or phrases; they warp in meaning compared with the original version.

This hasta X construction has been further naturalized into English by people using a target X that is not even Spanish. Perhaps influenced by the famous movie phrase “Hasta la vista, baby” from Terminator II, people also sometimes say:

Hasta la bye-bye

Which makes no sense at all, but they say it anyway. So you could even consider hasta X as moderately productive in English. If you’re into rhymes, then

Hasta la pasta

also works. In English it would probably mean “till supper” with pasta having the English sense and so here used as a tongue-in-cheek metanym — although in Spanish it could carry other meanings because pasta has more meanings there than it does in English, including slang for money.

In fact, hasta has become so common in English here that people say simply Hasta as a general sign-off without specifying until when:

Hasta!

I have never heard it used that way in Spanish, only in English.

I cannot tell you whether it is appropriate in casual speech in your own social circles. But clearly your colleague is comfortable with it, even in writing, so that perhaps tells you something.

Note that the English pronunciations are also somewhat naturalized into English from the original versions, since both of the two most common ones (hasta la vista, hasta luego) contain sounds in Spanish that do not even occur in English.