Why was it acceptable to provide the alternative timeline with trans-warp beaming equations/formula?

It was not acceptable. As a matter of fact, it was in direct violation of the Temporal Prime Directive - Regulation 157, Section 3 (Paragraph 18): Starfleet officers shall take all necessary precautions to minimize any participation in historical events. (DS9: "Trials and Tribble-ations")

• Federation Temporal Policies normally forbid any time traveler from interacting with or changing through action, any period, past or future by a member of Star Fleet.
• The goal of the Temporal Prime Directive is to maintain the future as it was known and to promote a future which ensured the continued existence of the Federation.

The Temporal Prime Directive was a fundamental Starfleet principle.

All Starfleet personnel are strictly forbidden from directly interfering with historical events and are required to maintain the timeline and prevent history from being altered. It also restricts people from telling too much about the future, so as not to cause paradoxes or alter the timeline. The Temporal Prime Directive is directly related to the Prime Directive.

So why did he do it?

• From Prime Spock's perspective, the timeline had already suffered catastophic changes with the arrival of the Narada from the future-Prime timeline. Mere scans of the ship had carried a variety of future tech to this new timeline, at a far earlier period than they were previously developed.

• Along with the harm the Narada caused, the ships it crippled or damaged in battle and with the destruction of Vulcan, Prime Spock thought he would be able to mitigate further damage to the timeline by bringing Kirk and Spock back together.

• Prime Spock reasoned that like in his timeline, the interactions of Kirk, Spock and the legendary crew of the Enterprise would be enough to stop the Narada and prevent further temporal contamination or the destruction of Earth and the heart of the Federation.

From our perspective, this new timeline bears less resemblance to the Federation of the Prime Universe but the Federation still exists and since Prime Spock did not appear to be able to return home, he considered the use of the Trans-Warp beaming technology to be a viable price to pay to save the Federation at large. He probably believes the Federation will grow to resemble his Federation farther into the future.

It was not an ideal situation, nor choice, but if the Temporal Police still existed, they would probably be forced to allow the changes which took place because they were part of a major transformative event. Unfortunately we don't know if the Temporal Police will exist/do exist in the Star Trek 2009 universe's future.