If I am not wrong the above topology matches with your query ?
If that said then if the redistribution is being done by DLR then the FA must be 126.96.36.199 ( Which will describe DLR identity )
So from Link state protocol it makes sense, which will go through recursive routing process and when processing traffic for 192.168.1.0/24 it will do recursive routing for ASBR which is 188.8.131.52
This is the output what I got when checked on Cisco RTR:
RTR22#show ip ospf database external
OSPF Router with ID (10.21.22.22) (Process ID 1)
Type-5 AS External Link States
Routing Bit Set on this LSA in topology Base with MTID 0
LS age: 641
Options: (No TOS-capability, DC, Upward)
LS Type: AS External Link
Link State ID: 192.168.1.0 (External Network Number )
Advertising Router: 184.108.40.206
LS Seq Number: 80000001
Network Mask: /24
Metric Type: 2 (Larger than any link state path)
Forward Address: 0.0.0.0 ( I hope this got changed in NSX setup to DLR IP )
External Route Tag: 0
0.0.0.0 here means to look to advertising router which is recursive routing , but when NSX advertises it makes the recursive lookup simple.
I hope this answer your query.