It sounds like you should read up on Import Records. This is a tool that you can use to move records (including your pictures) from one table to another in the same file or different files. There's also a "new table" option that can be used to create a new table as part of the import process.
You can learn more about the various options for Import Records in the Filemaker Help system.
I read up on Import Records. Unfortunately, since I'm using the ApertureToFileMaker plugin, I'm technically exporting from Aperture to FileMaker. So I never see an Import Field Mapping dialog box (or any dialog box, for that matter).
I'm assuming this means there is no way for me to re-route my photo files while they are being exported from Aperture into FileMaker. But is there some way to move the files from one table to another once I've brought the files into FileMaker?
I am not familiar with the plugin (or with Apperture), so I don't know how that works. However, I'd advise you to keep all your photos in the same table, and use a field in this table to indicate the album. It would probably be best to have another table for the albums, with a one-to-many relationship to the Photos table.