Hi Wd,
In order to get VLANs communicating between switches, you will need to configure VLAN tagging (802.1q) often called VLAN "trunking". You will need to configure this on both sides.
From device manager be sure to enable the fiber port as a "trunk" port, and then add that port to the 10 VLANs that you'd like on the 380-24F (or whatever subset of the 10 thats relevant for that connection).
On the remote side, you will also need to configure the 802.1q VLAN tagggin/trunking protocol with same VLAN IDs on whatever switch you are using. If the switch does not support 802.1q then, unfortunately, this will not work.
I hope this info is helpful.
-HH