I have hypothesis not tested enough yet.
For the correct conversion EPS file into JPG file preview, it must contain the entry:
If "StartupProfile" is not set to "Basic RGB" or the entry not present at all, conversion may produce faded colors.
It looks like Alamy converter is strictly guided by "StartupProfile", while Photoshop and Shutterstock converter simply ignore it.
To make sure that "StartupProfile" is set to "Basic RGB", you have to create a new Illustrator document from scratch (as "Basic RGB") and then cut and paste your vector design there.
It is curious that any change of colour mode during subsequent work in Illustrator does not change "StartupProfile" setting, it remains the same.
Ready-made EPS files can easily be checked with a simple text search "Basic RGB" in it.