It looks like Oil is getting past the seal.
there are two probable potential causes.
1 The vent is plugged and as the diff warms up it pushes oil past the seal. This can be checked by removing the vent hose at the diff and seeing if you can blow threw the hose.
2 The seal is leaking. Probable cause is an assembly issue like it’s installed crooked or it has pushed out from where it’s supposed to be. More difficult to check, it needs some disassembly to check.