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Note: when I mention the name of a note in this question, I'm referring to the saxophone pitch, not the concert pitch.

I play the alto saxophone, and lately I've been practicing mostly with a tuner. My instructor recommended that I start tuning to C# rather than G. I've taken the advice and started tuning to C#.

Once thing I've noticed now that I'm playing with a tuner is that, when I tune to G, playing C# sounds really flat. As in, halfway to C♮ kinda flat. It happens the other way, too: tuning to C# makes every other note sound extremely sharp.

When it's tuned to G, every note sounds perfectly normal and in-tune, except for C#. I don't know a whole lot about how instruments actually work, but I would guess it has something to do with C# being played completely open.

Is there a reason behind this? How can it be fixed?

The all-open C# is a tricky note on all saxophones. It tends to be very flat compared to the other notes, but it is also very sensitive to changes in embouchure. Personally, I don't think it is a great note to tune to on saxophone. When possible, I produce this note by use the low-C# fingering with the octave key pressed down. The tone of this note can be quit different from the nearby notes, so I don't usually use it from scalar passages.

G above the staff, on the other hand, tends to sound be fairly sharp compared to the other notes on the horn. When I play that note, I am always conscious to drop my jaw as much as possible to bring it in tune. Unfortunately, I don't know of any alternate fingerings for that note. Personally, I don't think it is a great note to tune to on saxophone.

Concert bands tend to tune to concert Bb - G on alto and C on tenor. I find that this works alright on my tenor, but as I said above, I don't think G is a very good note to tune to. Nonetheless, if you play in any kind of concert band, you will probably need to do it anyway.

I usually tune my saxophones to concert A - F# on alto and B on tenor. This note is the standard for orchestras around the world, so I figure it's good enough for me, and it puts most of the notes on all horn in tune for me.

Note: the relative pitches of saxophones will vary depending on the make and model, and even varies from horn to horn, so take my advice with a grain of salt.