How exactly were they inflated?

The monthly employment numbers the BLS publishes are basically nonsense and I'm sure they wouldn't publish them if Congress didn't force them to. At the middle of every month, they run a survey asking ~120,000 businesses how many employees they had as of the 12th of the month. It takes 8 weeks for all the responses to the survey to come in, but the initial monthly numbers are based off of the first 2 weeks of responses. This initial data is always more representative of larger companies. The BLS then generally issues two corrections to each month's data, one when all the responses to the surveys come in and the other when they get the actual unemployment numbers from quarterly unemployment insurance tax filings.

We see large corrections in employment numbers when there's rapid changes in the job market that mess with the models, or when the changes are focused towards small companies. Right-wingers have somehow decided that all of this is instead due to the BLS somehow being out to get Trump, despite there being no significant changes to how the jobs report is made since the mid-90s.