Practically speaking, there are usually committees (may be area specific, or general such as scheduling/introductory) that make the first choice as to how the process will continue. For new york this seems to be the standing committee which decides what will be put to a vote, “ Members of Standing Committees evaluate bills and decide whether to "report" them (send them) to the Senate floor for a final decision by the full membership.”[0].
I would like to know who the governor made an agreement with. The Standing Committees might be a possibility. kwiens named the bills sponsors as a possibility. (https://news.ycombinator.com/item?id=34193369). If the bill was changed shortly before signing it, i would also like to know what the text of the signed bill is. This whole process implied by memorandum #93 seems irregular to me.
Stuff like this should be documented publicly, IMHO.