Since the entire structure of ISS is not perfectly symmetrical and that the thrust vector produced during firing up of Soyuz thrusters/engines during altitude correction, is not perfectly aligned with the centre of mass of ISS, does such manuevers induce a slight spin to the station, which might be later corrected by attitude stabilising thruster?
ISS reboosts are typically done by Progress logistics resupply vehicles, not Soyuzes.
The Progress provides three-axis control during the reboost burn by firing its attitude control thrusters. There are no significant residual rotational rates after a properly executed reboost.
The Service Module provides control in all three axes (although its roll control is not particularly efficient), and a Progress or an ATV at the SM -Aft docking port can provide control in all three axes as well.
Although no further flights of the European ATV are planned to the ISS, the referenced paper gives an idea of the relative magnitude of propellant used during reboost for altitude raising vs. attitude control.
Three ATV vehicles - Jules Verne (2008), Johannes Kepler (2011) and Edoardo Amaldi (2012) – together performed a total of 25 maneuvers to provide 67 m/s of ISS reboost at an expense of 8400 kg of propellants. Attitude control propellants during these reboost maneuvers accounted for an additional 1926 kg.
Do such manuevers induce a slight spin to the station, which might be later corrected by attitude stabilising thruster?
This is not done after the fact. It is done while the spacecraft is firing its thrusters.
Any spacecraft, not just the ISS, is subject to cross coupling where thrusters fired to produce a desired force also result in an undesired torque. Cross coupling where thrusters fired to produce a desired torque also result in an undesired force also occurs.
The ability of the spacecraft to counteract these undesired torques and forces while the thrusters are active is one of the key aspects investigated during the design phase of the spacecraft. The spacecraft control system must be able to counteract these undesired rotational and linear accelerations at all times.