Under 42 C.F.R. section 70.6, the actual authority to issue a quarantine order (or an isolation order, or a conditional release order) is delegated to the director of the Centers for Disease Control and Prevention (CDC).
Once the decision is made, Trump has the power to declare an enforced quarantine under Public Health Service Act and under the 10th Amendment.
What are the penalties for disobedience?
If convicted of violating a quarantine order, a person can be sent to jail for up to a year (see 42 USC § 271(a)).