Everything in the data table is timestamped in UTC. The timestamp is then converted into the local time as set for that participant's account.
Each survey instance is identified in the system and the Flat Data File by its "Start Time", i.e. the time the notification alert was first sounded on the phone. On-Demand type surveys are timestamped at the moment the user presses the green plus sign next to the survey in the app.
Note: If a survey is completed before it's scheduled time, then the instance will still be logged in the data file as occurring at the time it was scheduled for (this is only possible if the time window is set to open before the assignment).
On the participant's Survey Assignments page, in the Instances table you will see an "Instance ID" column. That is the timestamp of the survey instance.
When you view the same Instance as part of the Flat Data Table 
from the Survey Editor you will see the same timestamp again (in the second column). It is expressed in UTC (Coordinated Universal Time). If you select the option "local TS" before you load the Data File then the third column will show the timestamp captured from the phone at that moment.
Note: If the participant is in the same time zone as the setting you made on their My Surveys page then these two timestamps will be the same. However, if they are in another time zone then they will differ. The timestamp in the flat data file is most accurate because it is taken directly from the mobile device rather than being something you can set.
ilumivu can provide a report showing the timestamp of every touch your users made in each survey. This is provided as part of the Professional mEMA License. Please contact your account manager for more information.