In my opinion it's a bug. However no matter what I do I can't reproduce this behavior.
I've tried with a clean FlashFXP.ini and my results are totally different.
After connecting to site C, site B will list and then Site C will list.
[08:50:56] [L] QUIT
[08:50:56] [L] 221 Come back soon!
<--- Disconnect site A
[08:50:56] [L] Logged off: 10.1.1.20
[08:50:56] [L] Connecting to File Server -> IP=10.1.1.50
[08:50:56] [L] Connected to File Server
.......
[08:50:56] [L] CLNT FlashFXP 3.3.7.1131
[08:50:56] [L] 200 Noted.
<--- Site C logged in
[08:50:56] [R] TYPE A
[08:50:56] [R] 200 Type set to A.
[08:50:56] [R] PROT P
[08:50:56] [R] 200 PROT command successful.
[08:50:56] [R] PASV
[08:50:56] [R] 227 Entering Passive Mode (10,1,1,50,234,197)
[08:50:56] [R] Opening data connection IP: 10.1.1.50 PORT: 60101
[08:50:56] [R] LIST -al
[08:50:56] [R] Connected. Negotiating TLSv1 session..
[08:50:56] [R] 150 Data connection accepted from 10.1.1.10:4630; transfer starting.
[08:50:57] [R] TLSv1 negotiation successful...
[08:50:57] [R] TLSv1 encrypted session using cipher AES256-SHA (256 bits)
[08:50:57] [R] 226 Transfer ok. [Free: 1.606 GBytes]
[08:50:57] [R] List Complete: 403 bytes in 0.05 seconds (8.4 KB/s)
<--- Site B refreshed listing
[08:50:57] [L] PWD
[08:50:57] [L] 257 "/" is current directory.
[08:50:57] [L] MKD /RichVideo
[08:50:57] [L] 257 "/RichVideo": directory created.
[08:50:57] [L] CWD /RichVideo
[08:50:57] [L] 250 CWD command successful. "/RichVideo" is current directory.
<--- Site C makes dir, etc
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