A clear example of the sequence for executing a mandate is on page 15 under MARSHAL, Example (bottom of page).
Rulebook, page 15 wrote:
[In this example, Dragonfly and Koi are allies. It is Dragonfly's turn. Seating order around the table is Dragonfly, Koi, Lotus, Turtle.]
EXAMPLE: The DRAGONFLY player plays Marshal, so they will perform it last. Going around the table, the KOI player gets to execute their Marshal actions. They Move a Bushi from Kansai to Nagato, crossing a Border. They also move their Oni of Blood and Daimyo to Hokkaido, using Shipping Routes. They decide not to Move the Bushi in Edo and wouldn’t be allowed to Move the Shinto which is in the Raijin Shrine (figures on the Shrines can never be Moved).
Finally, since they are Allied with the DRAGONFLY Clan, who chose the Mandate, they get to perform the Marshal Bonus, spending 3 Coins to build a new Stronghold in Shikoku.
Note that the Koi ally takes it's turn in seating order, immediately after Dragonfly. And it performs the Ally bonus at that moment, before other players execute the mandate.