It sounds like the VPN tunnel is setup as "tunnel-all" which will send all traffic over the VPN tunnel, including internet/O365.
Your ASA is also probably not setup to handle the required intra-interface routing and ACL/NAT to allow VPN connections coming in from the Outside interface to go back out the Outside interface for internet.
The solution is to ensure same-security-traffic permit intra-interface, ACLs, and NATs from OUTSIDE to OUTSIDE are configured.
Alternately, some might recommend a split tunnel whereby only internal networks go across the tunnel, but I would avoid this for security reasons unless you have an off-VPN security mechanism in place (host-based IPS, firewal, Umbrella, etc.).