I have issue on sending mbox parameters. It is kind of cross domain. In this use case , journey start with domain A and end with domain B. From domain B we are passing order confirmation mbox parameters to profile scripts. Since it is third-party domain I think those parameters are not sent properly to Adobe target.
Any idea or do we need to enable anything for this cross domain scenario?
Are your sites using ECID/Visitor ID Service? Are you using at.js 1.x or 2.x? If 1.x is Target using the default 1st party only cookies setting? The answer will vary depending on these circumstances.
With ECID in place if the visitor's browser accepts 3rd party cookies then as @Eric_Vidana mentioned if you use the same Target library (at.js) on both sites the same visitor should be linked across domains.
If you don't use the ECID and use the default Target implementation cookie method (1st party only), then the visitors on Domain A will appear to Target as a new visitors when they reach Domain B.
Keep in mind at.js 2.x ONLY supports 1st party cookies (help doc). So with at.js 2.x and no ECID cross domain visitors will appear as new visitors. Though you might still be able to pass the mboxSession as query parameter in a link from Domain A to Domain B and stitch them. I haven't tried this myself on at.js 2.x, but it could work. Of course, that only works when the visitor is changing domains through a link you control.
As long as you have the same Adobe Target library on the sites and they are both going to the same client endpoint, you should be fine. There are some settings in the Target interface to block/allow different hosts, but that setting is off by default. In addition, new requests should automatically be classified as production (Hosts settings) so you should be good there too.