Nikolai was 'encouraged' to have liasons before his bethrothal to Alix.
Mathilde K. in her own memoirs Dancing in Petersburg, she wrote of one occassion (p 63), when the now married Emperor transmitted a message to her via G. D. Serge Mikhailovich, providing the time he would pass by her residence in Strelna. At the given moment she curtsied at his approach, while he provided some gesture of acknowledgement. This is hardly a suggestion of a continuing passionate afffair.
There was never a question of impropriety. All encounters at the Marinsky were done in the company of Nikolai's retinue, and never alone. For Mathilde, his very attendance at the ballet to watch her perform Excelsior exhilarated her (p 93), to the extent she believed it was she who was responsible for the presence of the Emperor.
Although somewhat deluded, her affections were one-sided. I believe Nikolai was just extending a special degree of courtesy and politeness befitting his role, nothing more.
Many years ago I learned of rumors drifting within the Russian community that Andre's son Vova, was actually Nikolai's. However it is just another one of those myths some people enjoy manufacturing to discredit the name of the Emperor.