One aspect of FEA modeling that may not be obvious to a new user is the idea of of the zero stress state of a part. You show in blue, Axial Displacement #1, with a curved shape that you want to push axially and contact the yellow part. The problem is that the tube started out life as a straight tube. That is the shape it is in when it is manufactured. You have to bend it into the curve shown in blue before you start to push it axially. While you could draw the tube as curved in the CAD system and mesh it and start to push it axially, that simulation would behave differently than a tube that started out straight in a horizontal line, was bent into the curve and then pushed axially. The reason it will behave differently is the state of stress in the tube after it is bent will affect how it deforms when it makes contact with the wall.
You have been drawing straight tubes and trying to bend them, so maybe you already understood this concept.
When you take a straight tube fixed at one end and apply a 90 degree rotation to the other end face, you can get a nice circular shape. There is an APDL command snippet that allows the current position of a specific degree of freedom of a node to be fixed at the current position. That could be used on the end of a straight tube along the X axis after it has been bent into a curve to hold the node fixed in X at whatever value that was, while moving the node in the Y coordinate from wherever it was at the end of step 1.
When you say axial, you mean that it is following the path of the tube in a channel in the salmon part. I can imagine modelling the salmon part as a two-piece rigid form. Initially, the right part with the concave face is retracted way to the right. The left part with a convex face is fixed and the straight blue tube is pulled down to make contact with the left part in step 1. In step 2, the right part of the salmon form is translated to the left into place as shown above. In step 3, the tube is pushed and now has a path to follow, and freedom above the salmon part to deform as it makes contact with the yellow part.