When looking at a negotiation in IKEView, the "arrow" indicates who initiated.
==> means the local GW initiated
<== means the peer initiated
When looking at "vpn tu tlist", you'll sometimes see "No outbound SA" when IPSec negotiations have failed, but IKE succeeded. "vpn tu tlist" shows the outbound SA we use to encrypt traffic to the peer - it doesn't care which side initiated the negotiation.
Considering the peer is rejecting a proposal for the public IP of your gateway to their internal network, there is most likely have a Hide NAT configured on your internal network, and the peer is not configured to accept proposals from your public IP.
If this is an Automatic NAT (NAT configured on a host/network object directly), you can use the "Disable NAT inside the VPN community" setting under the "Advanced" settings of your VPN community. If you're using manual hide NAT rules, you'll need a no-NAT rule above your hide NAT rule.