Basically I'm saying that you have to complete your initial ADSO before starting fellowship, but you don't necessarily have to complete it before signing for the MSP.
From the Special Pay Guidance document:
D. MULTIYEAR SPECIAL PAY (MSP):
1. Annual payment amounts for multiyear contracts will be in the amounts indicated at Table 1. Officers may be paid at the rate for any specialty for which they are currently credentialed, but the MSP and incentive special pay (ISP) specialty must be the same.
2. Eligibility. A Medical Corps officer:
a. who is below the grade of O-7, and
b. who has a current, valid, unrestricted license or approved waiver, and
c. who has at least eight years of creditable service, or has completed any active duty service commitment incurred for medical education and training, and
d. who has completed initial residency training, or is scheduled to complete initial residency training before October 1, of the fiscal year in which the officer enters into an agreement, and
e. who executes a written agreement to remain on active duty for two, three or four years that is accepted by the Chief, BUMED (or designee) , and
f. who remains privileged and practicing during the length of the MSP agreement in the specialty for which the MSP agreement authorizes member to receive payment for.
Note: Based on Service unique requirements, the Chief, BUMED (or designee) may decline to offer MSP to any specialty that is otherwise eligible or restrict the length of an MSP contract for a specialty to less than four years.
3. Subject to acceptance by the Chief, BUMED (or designee), a medical officer with an existing MSP contract may terminate that contract to enter into a new MSP contract with an equal or longer obligation at the MSP annual rate in effect at the time of execution of the new MSP contract. The new obligation period cannot retroactively cover any portion or period under the old contract that was already executed.
4. Active duty service obligations for MSP will be established as follows:
a. Active Duty Obligations (ADO) for education and training and previous multiyear pay agreements will be served before serving the ADO for MSP. The MSP ADO is served after (consecutive) any other existing ADO for education and training has been completed.
b. When no education and training ADO exists at the time of an MSP agreement execution, the ADO for MSP is served concurrently with the MSP agreement period and all non-education and training ADOs. Also, if the MSP agreement is executed before the start date of fellowship training and no other education and training ADO exists, the MSP ADO is served concurrently with the MSP agreement period. However, if the MSP agreement is executed on or after the start date of fellowship training, the physician is obligated for the full fellowship period and the MSP ADO will begin one day after the fellowship ADO is completed. Once a physician has begun to serve an MSP ADO, it will be served concurrently with any existing ADO including obligations for other special pay agreements or medical education and training obligations incurred after the execution date for that particular MSP agreement.
c. Obligations for Additional Special Pay and Incentive Special Pay may be served concurrently with any other service obligation.
d. The ADO for Special Pay, promotion, doctorate degree, master's degree, and non-medical military schooling will run concurrently with any MSP obligation.