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To expand on Andy's answer, the order determines whether you're applying a global or local rotation.

q3 = quaternion_multiply(q1, q2)

Here q3 is the local rotation of q2 on q1
or
the global rotation of q1 on q2

q3 = quaternion_multiply(q2, q1)

Here q3 is the local rotation of q1 on q2
or
the global rotation of q2 on q1

In your case, you wanted to apply a global rotation of q2 on q1 -
i.e. apply the rotation q2 according to q1's parent coordinate frame (the coordinate frame on which q1 was applied initially

Further reading / maths:
https://answers.unity.com/questions/810579/quaternion-multiplication-order.html# https://math.stackexchange.com/questions/2124361/quaternions-multiplication-order-to-rotate-unrotate/2125858#2125858

To expand on Andy's answer, the order determines whether you're applying a global or local rotation.

q3 = quaternion_multiply(q1, q2)

Here q3 is the local rotation of q2 on q1
or
the global rotation of q1 on q2

q3 = quaternion_multiply(q2, q1)

Here q3 is the local rotation of q1 on q2
or
the global rotation of q2 on q1

In your case, you wanted to apply a global rotation of q2 on q1 -
i.e. apply the rotation q2 according to q1's parent coordinate frame (the coordinate frame on which q1 was applied initiallyinitially)

Further reading / maths:
https://answers.unity.com/questions/810579/quaternion-multiplication-order.html# https://math.stackexchange.com/questions/2124361/quaternions-multiplication-order-to-rotate-unrotate/2125858#2125858 https://math.stackexchange.com/questions/2124361/quaternions-multiplication-order-to-rotate-unrotate/2125858#2125858