Long story short: they should be written in your tense, since they are actually written by you, on your behalf.

When asking an acquaintance for an intro, make sure you provide enough context for your acquaintance to justify making the connection:

- clarify how you're connected;
- mention the name of the startup and ways to look it up;
- include a very concise outline of what your startup's capabilities are and what you've achieved so far;
- end with a call to action.

Your acquaintance can then either forward your email entirely or use it to quickly put together a separate message based on the information you've already provided.