You probably want to apply vmbr0 instead of eth0 to your nat rule. I prefer to use SNAT in those situations, so you could alternatively try this:
post-up iptables -t nat -A POSTROUTING -s 10.10.10.0/24 -o vmbr0 -j SNAT --to-source 178.251.229.125
post-down iptables -t nat -D POSTROUTING -s...