Are Tharsis Montes and Hellas Basin a result of the same event?
You were not the first to have seen that the Hellas Basin and parts of the Tharsis Rise are roughly antipodal (Peterson 1978, Williams and Greeley 1994). The Tharsis Montes themselves are far too close to the equator to be considered antipodal to the Hellas Basin. The shield volcano Alba Mons however is almost exactly antipodal to the Hellas Basin.
This shield volcano is a bit to the north of the Tharsis Rise proper, and well to the north of the Tharsis Montes. Both Peterson and Williams suggested that the Hellas Basin impact might well have triggered the vulcanism that resulted in Alba Mons.
There's an issue with this hypothesis, which is that the apparent ages do not align. Improved remote observations of Mars has provided a tool for estimating ages of Mars features: crater density. Based on crater density, the Hellas Basin appears to be very old, at least 3.8 billion years old (Carr 2010). Alba Mons, while also quite old, isn't that old. It formed at least 200 million years after the Hellas Basin impact and perhaps as much as a billion years after (Ivanov 2006).
Bottom line: If the huge impact that formed the Hellas Basin did have any antipodal effects, those effects are buried under the magma that formed Alba Mons several hundred million years later.
Carr, Michael H., and James W. Head III. "Geologic history of Mars." Earth and Planetary Science Letters 294.3-4 (2010): 185-203.
Ivanov, Mikhail A., and James W. Head. "Alba Patera, Mars: Topography, structure, and evolution of a unique late Hesperian–early Amazonian shield volcano." Journal of Geophysical Research: Planets 111.E9 (2006).
Peterson, J. E. "Antipodal effects of major basin-forming impacts on Mars." Lunar and Planetary Science Conference. Vol. 9. 1978.
Williams, David A., and Ronald Greeley. "Assessment of antipodal-impact terrains on Mars." Icarus 110.2 (1994): 196-202.