KENNER, La.—More details emerged Wednesday about a disagreement between employees of rig operator Transocean Ltd. and oil giant BP PLC over how to begin shutting down the well just hours before it exploded in the Gulf of Mexico last month.

Testimony on Wednesday about the disagreement, in a hearing held by the U.S. Coast Guard and the Minerals Management Service, which jointly regulate offshore drilling, was likely to bring increased scrutiny to the decisions BP made aboard the rig the day of the explosion, April 20.

There...