I have an FME session set up, from shapefile to shapefile with a renamer. My number fields go in as "Long". They are set to come out as "Long". When I pull the output into ArcGIS, the format is "Double" What am I doing wrong?

You're probably doing nothing wrong, the differences between long and double data types are purely academic unless you're approaching the extreme limits of precision, i.e. you need more than 15 significant digits of decimal precision.

For the (very) curious: https://pediaa.com/what-is-the-difference-between-long-and-double-in-java/