If I were to code this program, I would start from the user's point of view, namely start appropriate action as soon as possible, such as when an error is discovered.
For the first part, the code is generally correct, but I suggest making change to avoid the following dialog:
Please enter Employee Name
Please enter Employee ID number
Please enter Hours Worked
Once the Employee Name is entered as -1, users expect to either quit the program or see the "goodbye" message.
They would be wondering what's the point of entering EmployeeID and hours worked, which are no longer relevant.
For number 2, it's a similar comment. In addition, the entry of EmployeeID can be modified to let the user immediately correct the ID right after he entered an invalid one, such as:
output "Please enter Employee ID number"
while EmployID is <1 or > 599
output "Incorrect Employee ID number, Please enter ID value 1- 599"
This will take care of the problem on the spot.
Otherwise, the pseudocode looks quite logical.
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