If a buyer wants part of the sale price to vest, is that normal?

Lets presume I'm going to sell my company for $1 million. Would it be normal for the acquirer to want to only pay $500K in cash and the other $500K after 1-3 years of being employed by them? In such a case what happens if before the time is up I decide to leave to pursue another opportunity?

Apart from a possible acqui-hire, many people also link part of the purchase price to if certain business goals are met in x amount of time. There are many deals where the founder stays on for another year to help with the transition process and do what they were doing with the business as planned prior to the acquisition.

This is more standard that you'd realize, and it makes perfect sense. Someone paying for your company wants to ensure they know how to run it like you did.

The scenario you appear to be talking about is an acqui-hire. They are buying the company AND you - and therefore they want to lock you in, to prevent you quitting. This is certainly not unusual.