It's best to use a pantone color when matching colors. CMYK and RGB are not finite enough to have predictable outputs between devices, RIPS, design applications and medias. Most RIPS will have spot color mappings tuned with the ICC profile to produce the truest match to the spot color book.
There are still factors such as pass counts, resolutions, color space, rendering intent, and a long long list of other small differences independent of the ICC which can modify colors. The best practice is to develop your profile for your specific media which produces the closest match to a defined color matching system such as Pantone, print the color chart, and use the color chart to reference the appropriate color during art creation. In theory most output which are tuned properly will have similar and predictable outputs when using a color matching system. Of course most probably are not tuned so your mileage may vary.
If you are the only one printing the output then you could choose to use a CMYK and RGB color chart, output the color chart, and use those specific colors just like the spot color chart. However, if you are going to have someone else output, or a separate RIP, then you will most likely have shifting color output when using CMYK, especially if there are mixtures of RGB, CMYK, Gradients, and Text.
Rendering intent starts to get a little messy during this scenario, which may be exactly your issue with your current situation. Make sure the color space (Adobe RGB 1998, vs sRGB..) and that all your rendering intents are are the same as the profile within the rip.
Also, if you are using FlexiSign Rip and Print then always 100% of the time select the Preset from the drop down menu even if it is displayed already or "Default". Some settings from the presets are not fully implemented until you re-select the preset. Very important to do this.
