On 6 August 2020, Akhmat Grozny announced the signing of Putsko to a two-year contract from Ufa.[3]
On 12 January 2024, Putsko's contract with Baltika Kaliningrad was terminated by mutual consent.[4] The following week, he joined reigning Armenian Premier League champions Urartu.[5] Putsko was coached 10 years earlier at Spartak youth teams by Urartu's manager Dmitri Gunko.