It appears that Mesh Models do not perform transitions on their own (transition handling is not part of model itself).
Is this feature missing and is it planned to add it to nRF Connect SDK?
Also I noticed that DTT model does not set default transition time for models in succeeding elements (e.g. it sets default transition time for Lightness in the same element, but not for CTL temperature in the following element). According to Mesh Model specification: "If a Generic Default Transition Time Server model is not present on the main element of the model, then the Generic Default Transition Time Server model instance that is present on the element with the largest address that is smaller than the address of the main element of the node shall be used;"
nRF Connect specification says that "The DTT Server provides a common way to specify the state transition time for other models on the same element.". So seems that single DTT model approach for models in following elements is not supported by SDK.