Hi,
why should the BIG-IP send a TCP Reset? A TCP Reset is sent, i.e. when a listener is closed or just not there (as long as the system is able to respond, which is of course not possible during the reboot).
The BIG-IP does not indicate a failover to the client. There is no reason for this. Active Connections may break, when they are not mirrored to the standby node, and if the protocol or application used is not able to re-initiate the connection without producing errors, like databases with their persistent connections. But especially this depends on your topology and configuration or virtual server type.
Please refer to https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/bigip-device-service-clustering-admin-11-6-0/6.html
Regards,
svs