With two equal cost paths, they both will be installed to the routing table (the FIB). Routing is based on destinations, not sources. You need PBR for source based routing (don’t do PBR; it’s an endless pit of trouble unless you absolutely positively must). Even source NAT doesn’t solve the issue.
If you want to ensure a packet travels via a predetermined path then you don’t have ECMP anymore. You can use BGP path attributes to influence path decisions between ASNs if you need that. Local_Pref, AS_Path, and/or Weight (locally significant to the router only) to exit an AS; MED to enter an AS.