I remove the seeds from the chilli and dried chilli so that the chilli paste will be very smooth rather than full of seeds. I'm sure you don't want to be biting into chilli seeds all the time while eating the mee siam!
For chillies, just cut them open and remove the seeds.
For dried chilli, cut it into segments and scald in hot water. This is to clean the dried chilli and make it easier to blend. It also helps to remove some seeds. You will have to cut open the dried chilli to check if there are leftover seeds before blending - personally, removing the seeds of dried chilli is my most dreaded step for this dish! Wear gloves if you've got sensitive skin.