Your flight into a country is booked with one airline. Your flight out is with another. That is not automatically a problem. The important part is having clear evidence of the onward journey when it is requested. Two airlines do not need to share one booking reference for your travel plan to make sense.
Why the second flight may be invisible
Airline booking systems are designed around reservations. If you purchase Madrid–Kuala Lumpur through one airline and Kuala Lumpur–Bangkok separately through another, you can end up with two confirmations, two booking references and two different places to manage the journey.
British Airways explains that flights booked under separate references are treated as separate journeys, even when the flights are operated within its own group. Its booking guidance also notes that travel-agent and partner flights may not all appear in one Manage My Booking view.
So if someone says, “I can only see your arrival flight,” the sensible next step is to show the second booking on its own terms: airline, passenger, departure airport, destination, flight date and reservation or ticket details.