Joists and beams are sized based on 3 conditions: 1) bending, 2) shear, and 3) deflection. However, only one of these elements will “govern”. That is to say, one will fail before the others.
Long spans usually fail in bending or deflection, while short spans with heavy loads fail in shear.
Adding smaller boards to existing joists is called a “composite” joist. Each member has certain characteristics and determining how (and where) to fasten them together is critical.
If additional boards are not added uniformly then the joist can be eccentrically loaded, which will cause it to twist and possibly fail.
Because of the complexity of calculating these loads (and connections), generally we design joists so loading is evenly distributed to the top of joists (and sistered joists) so the load is applied uniformly to all members. Therefore, we like all members to align on top. If one member is smaller (or has many knots and is not as good of grade) it doesn’t matter, as the load will transfer to adjacent members.
Also, your question about sistered joists not “going the full length” is important, because when joists bend they have tension on the bottom edge and compression on the top edge. So, if the sistered joist is not continuous on the bottom, then it can’t carry the tension throughout the joist. But if it’s discontinuous on top, the ends of each piece just presses against one another and is effective...if ends are pressed against each other tightly.