I run a sandbox campaign. Early on, the players got involved in a murder mystery simply by arriving at the location where a murder was about to be committed.
I don't know where this line of questions will go, but I'm hoping it reveals ways that a timeline or murder mystery can fit in a sandbox.
How did you determine the murder was going to happen?
Was it planned before the session?
Was it trigger based (you had notes that said "the day after the PCs show up, this NPC is murdered")?
Was it something you made up on the fly, as it made context within the session?
Does a timeline of planned events interfere with a sandbox?
What I mean is, between sessions, it's pretty easy to look at what the PCs did, and make adjustments to the world, move stuff around, make up new content as "reactions". If the PCs clear out a dungeon and 6 months go by, you can fill it with something new. If they whacked an overlord, somebody new fills in the vaccuum.
To the players, that looks like it was all planned and after the fact, there's a cause and effect and order of events.
Within a session, moving some orcs around, because they heard a noise in the dungeon, or the guards didn't report in also make sense, and the players might think there's a timeline, but there's not.
Running an actual timeline is a lot trickier, because a deviation early on can change everything, throwing off a chain of thought the DM had (which I believe can cause railroading).
Consider:
the butler (who will be the murderer) knows the household goes to sleep at 10PM.
at 10:30pm, he grabs the candlestick from the dining room
11:45 he listens at the master's door for snoring
11:55 he opens the door and sneaks in
12:00 he strikes with the murder weapon, killing the master
12:05 he wipes down the candlestick (missing a bit of blood in a groove)
12:10 he joins some stable hands in a game of poker, as an alibi, knowing they don't tell time too well
2:00AM he puts the candlestick back in the dining room
8:00AM the maid discovers the master is dead
9:00AM the inspector arrives to examine the scene
I'm not saying a murder mystery is run this way, only demonstrating a timeline for a murder, pre-PC interaction.
If the PCs are staying at the house that night as in Nagol's example, the original "murder timeline" might play out that way. It's even possible to abjudicate that the PCs slept through the murder like everybody else and awake in the morning to deal with the environment of the murder mystery itself.
However, its also possible (especially in a more complex case) that the PC are active, and thus can alter the timeline. That in turn presents a challenge in a complex case where the DM has built a mystery to be unraveled by controlling the variables to set it up.
Basically, a timeline before the PCs get involved is no big deal. That's fluff to help the DM make it make sense.
A timeline woven around the PCs is a bit more complex and might have some non-sandboxiness to it.
I might also note that a timeline is not the same as a time limit. The murderer having a ticket to board a train at noon tomorrow or the room filling up with water is a time limit. Time limits are fairly easy to abjudicate. WHereas each element in a time line assumes the outcome of the previous elements. Change an element and the whole thing is at risk.
This is unlike a dungeon, where by DM laziness if a PC clears out room 1, it doesn't have to affect room 2.