The Hohmann transfer orbit (HTO) was first proposed as a minimum energy orbit (propellant expenditure) to change from planet to planet, such as from Earth to Mars. The origination and destination orbits need not be circular. This transfer orbit can also be used to go from low Earth orbit (LEO) to geostationary orbit or to change other orbital heights. HTO is defined as an orbit in which the ellipse of the orbit is at periapsis (perigee, perihelion, etc.) at the lower orbit and at apoapsis at the higher orbit, whether transferring up or down. Thus, inserting into HTO from the origination orbit is done 180 degrees away from inserting into the destination orbit, and insertion and arrival are tangent to both the origination and destination orbits.

At ExoMars arrival, Mars is around 135 (not 180) degrees from the Earth at launch, as shown below, taking less time to reach Mars than the HTO takes. Thus, the transfer orbit used is not a Hohmann Transfer Orbit, although it is elliptical (except for the adjustment made a few days ago, but the current orbit is also elliptical). Constant electric propulsion would not be an elliptical orbit.
https://www.youtube.com/watch?v=ZEb6kEKFuTk (1/2 minute)

As we can see, ExoMars did not leave Earth in an orbit tangential to Earth’s orbit.

I have not studied the orbital transfer that ExoMars is using to get to Mars, but my understanding is that the reduced travel time does not require much more additional propellant, overall, than the HTO would use.

There are three major phases in transferring between planets. Phase 1 is when the first planet’s gravity is dominant, phase 2 the Sun’s gravity is dominant, and phase 3 the destination planet’s gravity is dominant. The video above shows the entire transfer from the Sun’s point of view, but we could have looked at it from all three points of view.

Around the Earth, the probe starts at LEO at 5 miles per second. It is accelerated by 2 mps to reach escape velocity, plus another couple of miles per second to climb the Sun’s gravity well to Mars’ orbit.

Around the Sun, it takes an elliptical orbit toward Mars, slowing as it climbs (trading velocity for height from the Sun), then for ExoMars, there was the adjustment burn on July 27th, and finally arrival into Mars’ gravitational influence in late September or early October.

Around Mars, another burn is necessary to enter Martian orbit, but as seen from Mars, the probe is travelling at escape velocity, and the probe has to slow down relative to Mars (the Sun would see it as speeding up) in order to get into orbit around Mars.

This link should give better details:
http://www.esa.int/Our_Activities/Operations/ExoMars_TGO_operations
“28 July (forecast): TGO carries out one of the most critical activities during the voyage to Mars: a very large engine burn in deep space that changes its direction and speed by some 326 m/s. This midcourse trajectory correction will line the spacecraft up to intersect the Red Planet on 19 October.”

As we improve space navigation and operations, with increasingly reliable spacecraft, we advance from flybys to complex maneuvers — including aerobraking — to reach the orbits we want.

Calvin Dodge: Do not assume that the length of this burn was because the spacecraft needed to make a gigantic correction. The length was determined by many factors, all of which appear planned, including the overall thrust of the engine itself.