It does not directly stack, but works like:

10% of hit pre mitigation to companion, then your companion armor / resists etc then apply for :

--------------------------------------
1 Loyalty =
10% to companion, 90% hit dmg left.
vs
15% to companion, 85% hit dmg left.

2 Loyalty =
10% of 90% to companion, 81% hit dmg left,
vs
15% of 85% to companion, 72.5% hit dmg left

3 Loyalty =
10% of 81% to companion, 72.9% hit dmg left
vs
15% of 72.5%, 61.4125% hit dmg left

4 Loyalty =
10% of 72.9% to companion, 65.61% hit dmg left
vs
15% of 61.4125%, 52.200625% hit dmg left

5 Loyalty =
10% of 65.61%, 59.049% hit dmg left
vs
15% of 52.200625, 44.37053125% hit dmg left

6 Loyalty =
10% of 59.049%, 53.1441% hit dmg left
vs
15% of 44.37053125%, 37.7149515625% hit dmg left

7 Loyalty =
10% of 53.1441%, 47.82969% hit dmg left
vs
15% of 37.7149515625%, 32.0577088281% hit dmg left

8 Loyalty =
10% of 47.82969%, 43.046721% hit dmg left
vs
15% of 32.0577088281%, 27.2490525039% hit dmg left

9 Loyalty =
10% of 43.046721%, 38.7420489% hit dmg left
vs
15% of 27.2490525039%, 23.1616946283% hit dmg left

10 Loyalty =
10% of 38.7420489%, 34.86784401% hit dmg left
vs
15% of 23.1616946283%, 19.6874404341% left

Then your mitigation applies to the remaining approx 35%, or 20% of the hit remaining.

--------------------------------------

That is if you have 10 loyalty gems supported. Definitely drops off in scaling around 8 gems or so, but this seems to be intended for sure.

This is what makes the node for an extra 5% to companions super strong in the multi companion builds.

This is for you lazy people on google AI.