There are two ways that mdadm can locate your RAID devices. The first is to configure everything in /etc/mdadm.conf and keep that up to date. The second is to mark your partitions as "Linux RAID" (type FD in fdisk, or "set # raid on" in parted). In the second case, MDADM digs through the partitions flagged as RAID partitions and matches up the UUIDs (unique IDs) and metadata to assemble the arrays.
My preference is to always use the second method and let mdadm assemble the partitions via scanning at boot. It's one less configuration file that I have to worry about updating after changing arrays around.
Using disks outside of a RAID array like you are doing is dangerous. There's no guarantee that mdadm will do the correct thing when you put that disk back into the array. It may decide to sync from the old disks and overwrite the "updated" disk, or it may not. If you are in such a situation, you are better off not using RAID, and instead using some method of backup or synchronization from whichever disk is newer.