Caching Bitcache files?

I am using Fle Framework / Bitcache to handle files.
The files served by this framework do not seem cached by Boost.

Below the http://www.webpagetest.org results:

1) for A small gif image

Performance

URL: http://www.see.asso.fr/sites/see.shareontheweb.com/themes/logos/NewSEE-50px.gif
Loaded By: http://www.see.asso.fr/:73
Host: www.see.asso.fr
IP: 37.187.137.19
Location: France
Error/Status Code: 200
Client Port: 3051
Start Offset: 0.459 s
Time to First Byte: 43 ms
Content Download: 0 ms
Bytes In (downloaded): 2.9 KB
Bytes Out (uploaded): 0.4 KB

REQUEST

GET /sites/see.shareontheweb.com/themes/logos/NewSEE-50px.gif HTTP/1.1
Host: www.see.asso.fr
Connection: keep-alive
Accept: image/webp,*/*;q=0.8
User-Agent: Mozilla/5.0 (Windows NT 5.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/33.0.1750.154 Safari/537.36 PTST/169
Referer: http://www.see.asso.fr/
Accept-Encoding: gzip,deflate,sdch
Accept-Language: fr-FR,fr;q=0.8,en-US;q=0.6,en;q=0.4

2) for a small FF file

Performance

URL: http://www.see.asso.fr/bitcache/6b329c9f02acae56440c83647c2cfa2ab4abaeb1?vid=16096&disposition=inline
Host: www.see.asso.fr
IP: 37.187.137.19
Location: France
Error/Status Code: 200
Client Port: 3054
Start Offset: 0.550 s
Time to First Byte: 301 ms
Content Download: 10 ms
Bytes In (downloaded): 4.5 KB
Bytes Out (uploaded): 0.4 KB

REQUEST

GET /bitcache/6b329c9f02acae56440c83647c2cfa2ab4abaeb1?vid=16096&disposition=inline HTTP/1.1
Host: www.see.asso.fr
Connection: keep-alive
Accept: image/webp,*/*;q=0.8
User-Agent: Mozilla/5.0 (Windows NT 5.1) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/33.0.1750.154 Safari/537.36 PTST/169
Referer: http://www.see.asso.fr/
Accept-Encoding: gzip,deflate,sdch
Accept-Language: fr-FR,fr;q=0.8,en-US;q=0.6,en;q=0.4

As you can see, content download is 10 ms in both cases.
However, time to first bit is respectively 43 / 301 ms, which badly affects speed.

How can I check if Boost really cares about these files, and if not, how I could make Boost caching these files as well?

Thanks for help