I am not sure I understand what you mean. Which sequence is supposed to be the out-group in the trees? In the 16S tree something is wrong with the sequence "gi|719240720|gb|KM114226.1| Demodex folliculorum mitochondrion complete genome". What method did you use to construct the trees and did you trim the sequences so that they are of similar legth?

In my view, first of all, you should remove part of sequence with poor Quality Value (QV) from your 1st BASE exported sequence. Take the part of sequence which has high QV (I hope, you did that already). Enter your sequence and check basic alignment by using blastn of NCBI (http://blast.ncbi.nlm.nih.gov/Blast.cgi?PROGRAM=blastn&BLAST_PROGRAMS=megaBlast&PAGE_TYPE=BlastSearch&SHOW_DEFAULTS=on&LINK_LOC=blasthome). See the BLAST result and find out whether your sequence has similarity with expected gene/organism or not. If it is showing similarity with unexpected gene/organisms; then you can assume that your sequence data has some problem.

If you have done all these things and found similarity with expected organism; then upload those reference sequences that have highest similarity with your sequence. Make necessary trimming and then make the phylogenetic tree.

I hope, this may help.

Anyway, can you please provide the length of your sequences, reference sequences that you used and percentage of similarity, etc? 

I agree with the previous answers you have received. Checking the quality of the sequences and the alignments is crucial to obtain a "correct" tree.

In the 16S tree, I would not say that one of your sequences is similar to the outgroup. I think you are probably looking at an unrooted tree, do not be mislead by the "artificial rooting" of the drawing. It looks like you have a long branch with one sequence (2241412 16S IVA 16 S F sequence exported from 1st BASE 2241412 16S IVA 16 S F.ab1).

To be able to help you better, it would be useful to know which was your aim when building these trees.