First let me say it is the first time I am using TAP (and not with Java). I do not know if the TAP results MUST match the Expected in test steps, and if the Jenkins username MUST match a user in Testlink.
I have the same problem, first with Jenkins 1.541 and Testlink 1.9.8, using TAP for shell scripts. Test builds are created in Testlink, but it shows always as no Run. After this attempts, also installed TAP Jenkins plugin, which shows correctly test runs.
I have upgraded Jenkins to 1.542 and TestLink to 1.9.9, and behavior is the same. Here is the final output of my shell script TAP:
Looking for the test results of TestLink test cases.

Found 1 test result(s).

TAP Reports Processing: START
Looking for TAP results report in workspace using pattern: *.tap
Saving reports...

Processing '/opt/jenkins/jobs/Gretl_builder/builds/2013-12-05_10-31-34/tap-master-files/build_gretl.tap'
Parsing TAP test result [/opt/jenkins/jobs/Gretl_builder/builds/2013-12-05_10-31-34/tap-master-files/build_gretl.tap].

TAP Version 13
1..3

1. Test-suite-name: build_gretl
2. Test-machine-name: candy-house
   ok - autoreport
   ok - gretl clean, configure, make and install
   ok - tapdata
   —
   tapdata: 1
   starttime: 1386239618
   endtime: 1386240198
   runtime: 580
   ...

Processing '/opt/jenkins/jobs/Gretl_builder/builds/2013-12-05_10-31-34/tap-master-files/cvsgretl.tap'
Parsing TAP test result [/opt/jenkins/jobs/Gretl_builder/builds/2013-12-05_10-31-34/tap-master-files/cvsgretl.tap].
TAP Version 13
1..3

1. Test-suite-name: cvsgretl
2. Test-machine-name: candy-house
   ok - autoreport
   ok - CVS updated sucessfully
   ok - tapdata
   —
   tapdata: 1
   starttime: 1386239563
   endtime: 1386239614
   runtime: 51
   ...

TAP Reports Processing: FINISH

Finished: SUCCESS

I have finally managed to get the TAP results synchronized with Testlink.
Instead of having two tap files, I redirected the output to a single file, matching the Custom Field value and file name. (Only the last step result is recorded in tap file). So would have to adjust test to only one step.

I have used Tapper (bash-test-utils) mentioned in http://en.wikipedia.org/wiki/Test_Anything_Protocol.
(my test is pure bash script: Step 1 - cvs update; Step 2 - make clean; ./configure; make; make install)
Redirected tap results to file ShellScript.tap, the same value excluding .tap as Custom Field and TAP Test Result Seeking Strategies *.tap and Custom Fields: ShellScript.

The use of */.tap as default value, made me think that it would accept several tap files. Can someone investigate the use of TAP reports from non Java classes, like the example I have posted, so that we could have better documentation?

Thanks,
Hélio

I updated the capture attachments, Could you help me to find the solution? Thanks in advance.