It is assumed that they were executed for having the decorations for Caesar's victory taken down from the statues of Caesar. This is mentioned in Act I, scene ii, when Casca reports:
"I could tell you more news too. Marullus and Flavius, for pulling scarves off Caesar's images, are put to silence."
Some scholars believe that "put to silence" means they were imprisoned or forced out of office, including the notes for David Bevington's The Necessary Shakespeare.
The time of day this occurred is unclear. If it was an execution, it would have to have been during the day sometime as it was public enough for Casca to be reporting the news alongside the news of Caesar's thrice refusal of the crown. If it was imprisonment or removal from office, it probably could have occurred at anytime.
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