If a uPaged facility has opted to employ uPaged practitioners, the hospital is your employer.
If a uPaged facility has opted to use uPaged to employ uPaged practitioners, uPaged is your employer.
When you are booked into a shift, the confirmation message in the platform will let you know the name of your employer as either the facility or uPaged.
uPaged shifts are casual shifts, so you will be asked to sign a casual contract with either of the above before your first shift. This means you become a casual employee of that facility or uPaged, so be sure to look out for an email from them. It could be in your junk mail.