You ask a good question. I have been on speaking panels with other lawyers on the independent contractor vs. employee issue for years, and I can honestly say I still do not have all the answers for whether you are classified correctly.
We lawyers go through the 20-factor test, focusing on "control". If you imagine control as a "sliding scale," the more control the company has over your work hours and your work conditions, the more likely you are an employee.
I or another experienced lawyer would need to have a more in-depth (free consultation) with you to understand your classification better.
Assuming you are correctly classified as an independent contractor -- and that is a legal conclusion that I am not willing to make here based on the limited info you provided -- then you are left to your own devices to negotiate extra payment for training hours. It is a matter of contract.
Hope this helps.
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