The only way this can happen is if your co-artist already has a swatch by the same name in her document and then importing the swatch library created by you.
See if avoiding this solves your problem, otherwise let us know what exactly you are doing - saving a swatch library, ASE or AI, or simply opening the AI file created by your colleague.
Could it be that one of you has the Document Color Mode set to CMYK and the other to RGB? That'll give you color shifts every time.
No. We are both in CMYK color mode.
I created an AI file of the swatches and loaded it under Library > Application Support > Adobe > Swatches. We both did this.
When we opened the same file in Illustrator with both are getting different values on the spot colors.
There's a few things I can think of that might trigger this type of shift:
1.) The other computer is using Pantone Color Bridge as a default, whereas your computer is accessing the Illustrator installed Pantone Color System or vice versa. The "Bridge" CMYK equivalents have been reformulated and may or may not be different, depending on the actual Spot color.
2.) The other computer is using different color settings than yours or vice versa. This could also include system settings in ColorSync and/or Adobe's Bridge application, as well as Illustrator's application color settings.
It could be just a matter of confirming all of the settings are set the same on all computers and then see how the file behaves.