When does signaling for SegWit start exactly? I thought that signaling for SegWit (and other softforks deployed by means of BIP0009) would start with the first block after the Starttime defined in the BIP is reached.

Someone claimed that it only starts with the first difficulty retarget after the starttime. Is that true?
Signaling will commence with the first difficulty retarget after November 15th 12am UTC (i.e. midnight between 2016-11-14 and 2016-11-15).

See BIP0009 State Transitions:


  All blocks within a retarget period have the same state. This means that if floor(block1.height / 2016) = floor(block2.height / 2016), they are guaranteed to have the same state for every deployment. 


Which means that blocks will only switch state when a new difficulty period begins after the starttime.

This means that signaling for SegWit will begin sometime on the 19th in the afternoon (UTC). The earliest that SegWit could activate therefore is the 17th of December (two difficulty periods later).