Connecting transformers in parallel.Will this be a problem?
I am planning on using two transformers (in parallel) to create a positive rail and a negative rail. Will this cause a problem?


No. The primaries are in parallel as they should be. The secondaries are not.


  I have researched online and found that the transformers can be connected in parallel given that they have the same number of turns and are in phase.


That would be a requirement if you were connecting the secondaries together at both ends. You're not in this case and it would not be unusual to have different voltage requirements for the positive and negative rail and so different transformer secondary voltages would be used.


  Both the transformers will be connected to the same AC outlet thus I assume they would be in phase?


That depends on internal and external wiring of and to the coils but in this case it doesn't matter. At the output of the bridge rectifiers is a 100 Hz (assuming 50 Hz supply) full-wave rectified signal. This will be the same regardless of the input or output phasing.


  Also both the transformers are 220 V AC to 12 V AC , but one of them is rated for 1 A (planning to use that for +ve rail) while the other is rated for 500 mA. Will this cause a problem? I assume not since they would both have the same no of turns (the 1 A transformer may have thicker windings ?)


Your assumption is correct but your reasoning is not. As discussed above, your two rectified supplies are independent and only connected at one point. An analogy is a 12 V car battery for your positive supply and a small 9 V battery for your negative supply. If the 9 V battery can provide the required current on its load then that's all you need.


  Is my schematic correct? I think this is how to create a negative voltage rail.


Yes. You'll probably be adding in some capacitors to smooth it out.