Do you know if GIT is trying to use a server name or an IP address to make it's connection? Contacting resources by IPv4 address will never work over a DirectAccess connection. DA is very different than an IPv4 Layer 3 VPN such as Checkpoint.
Try to make sure that GIT is configured to communicate with a DNS name, NOT an IP. For example, if you are trying to contact "Server1", when you "ping server1" you should resolve to an IPv6 address on your DirectAccess client. This would indicate that DirectAccess
is successfully handling your DNS request and spinning it through the tunnels. However, if you try to "ping 10.10.10.100" - this is never, ever going to work over a DirectAccess tunnel.