Ok, I think I got it right finally. I had to create two separate Sites, one for each AWS VPN tunnel:
It's worth noting that AWS considers Tunnel 1 to be the primary connection to use and Tunnel 2 is utilized only when Tunnel 1 is down. It achieves this by not advertising BGP routes to VPC's IP CIDR blocks via VTI of Tunnel 2, so our case the route to VPC's is only available via 169.254.192.145 (AWS side VTI's IP address). As soon as the IPSEC via Tunnel 1 is down, it start advertising the route via 169.254.249.253.
However, to make use of redundancy of AWS VPN's tunnels, you'd have to add an additional <site></site> section in your REST API body that would set up the second connection.
<?xml version="1.0" encoding="UTF-8"?>
<ipsec>
<version>38</version>
<enabled>true</enabled>
<disableEvent>false</disableEvent>
<logging>
<enable>true</enable>
<logLevel>warning</logLevel>
</logging>
<sites>
<site>
<enabled>true</enabled>
<name>Amazon_VPC_1</name>
<description>Route-based VPN to Amazon</description>
<localId>217.28.xxx.xxx</localId>
<localIp>217.28.xxx.xxx</localIp>
<peerId>13.48.xxx.xxx</peerId>
<peerIp>13.48.xxx.xxx</peerIp>
<ipsecSessionType>routebasedsession</ipsecSessionType>
<tunnelInterface>
<ipAddress>169.254.192.146/30</ipAddress>
<mtu>1500</mtu>
</tunnelInterface>
<encryptionAlgorithm>aes256</encryptionAlgorithm>
<enablePfs>true</enablePfs>
<dhGroup>dh2</dhGroup>
<localSubnets>
<subnet>0.0.0.0/0</subnet>
</localSubnets>
<peerSubnets>
<subnet>0.0.0.0/0</subnet>
</peerSubnets>
<psk>YoUr.FiRsT.kEy.HeRe</psk>
<authenticationMode>psk</authenticationMode>
<ikeOption>ikev1</ikeOption>
<digestAlgorithm>sha1</digestAlgorithm>
<responderOnly>false</responderOnly>
</site>
<site>
<enabled>true</enabled>
<name>Amazon_VPC_2</name>
<description>Route-based VPN to Amazon</description>
<localId>217.28.xxx.xxx</localId>
<localIp>217.28.xxx.xxx</localIp>
<peerId>13.48.xxx.xxx</peerId>
<peerIp>13.48.xxx.xxx</peerIp>
<ipsecSessionType>routebasedsession</ipsecSessionType>
<tunnelInterface>
<ipAddress>169.254.249.254/30</ipAddress>
<mtu>1500</mtu>
</tunnelInterface>
<encryptionAlgorithm>aes256</encryptionAlgorithm>
<enablePfs>true</enablePfs>
<dhGroup>dh2</dhGroup>
<localSubnets>
<subnet>0.0.0.0/0</subnet>
</localSubnets>
<peerSubnets>
<subnet>0.0.0.0/0</subnet>
</peerSubnets>
<psk>YoUr.SeCoNd.KeY.hErE</psk>
<authenticationMode>psk</authenticationMode>
<ikeOption>ikev1</ikeOption>
<digestAlgorithm>sha1</digestAlgorithm>
<responderOnly>false</responderOnly>
</site>
</sites>
<global><psk></psk><caCertificates/><crlCertificates/></global>
</ipsec>