Are you licensed in California?
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There are two issues: are you an employee or an independent contractor, and; if you're an independent contractor, then are you and/or the other attorney in compliance with the Rules of Professional Conduct concerning fee-splitting (2-200)?
On the first issue, a worker is an employee, if the employer has the "right" to control the "means and methods" of the employee's labor. That is, if the employer has the right to control "how" the work is done, rather than merely, the ultimate result, then the worker is an employee, otherwise, the worker is an independent contractor.
Diffierent agencies use different tests to conclude on this issue, but, you don't really need to concern yourself with that: you just have to complain, and if you do, for example, to the Division of Labor Standards Enforcement, and they will figure it out for you (of course, you can also sue privately, being that you're a lawyer, to advance your rights, rather than letting the Division handle the case, but that's up to you).
If you decide that you want to go the "independent contractor" route, then you are faced with the possibiity of having violated the Rules. Needless to say, neither you nor your adversary would bother mentioning this if you were to face of in court, because if one of you has violated the Rules, then so has the other -- but, I think it fair to mention this, because a judge could decide to mention the issue to the State Bar, in which case, you are both screeeewed (pardon my French).
In State Bar Formal Opinion 1994-138, there is an excellent discussion of the types of arrangements which would violate the Rules (see http://www.calbar.ca.gov/calbar/html_unclassified/ca94-138.html).
I won't bother to analyze your legal position here. You can do that as well as I.
However, I would say that if you billed hours to the attorney and the attorney billed the client for HIS time, rather than for yours, then that would make you an employee rather than an independent contractor, because the client knows nothing about you and you are entirely subject to the control of the other attorney.
Lawyer
Retired (mostly)