"obtained when" is correct and usable in written English.
You can use it when referring to the time at which something was acquired. For example: "The new documents were obtained when the team conducted their research."
The magic set was obtained when Teller was five.
His lawyer said licences were "obtained when required" from the Treasury.
Interestingly, exactly the same result was obtained when they were exposed to films with happy themes.
His previous urine sample, obtained when he was taking EPO, was negative in this lab's test.
The pictures were obtained when rebel leaders allowed two women to visit their imprisoned relatives.
The best result is obtained when.
Similar results were obtained when analyzing bladders.
Similar results were obtained when θ = 0.1.
Similar results are obtained when CD19-Cyt2 is expressed.
Consistent results were obtained when the reciprocal experiment was performed.
However, similar results were obtained when multiple episodes were analyzed.
