Fellows was a stockholder and officer of the company that strung the line from Jeff City to Springfield in 1859. He had business in Rolla and after Wilson's Creek removed from Springfield to Rolla. Might be a starting point for a hunt for info.
http://thelibrary.springfield.missouri.org/lochist/history/paspres/fellowsh.html
This source : "William R. Plum, The Military Telegraph During the Civil War in the United States (Chicago: Jansen, McClurg & Co., 1882), vol. 1 and 2." list C.S Payne as the operator in Rolla as of August 25th 1861.
Lists August 1861 as the line to Rolla being hung by a special signal corps battalion headed by a Maj. George H Smith. see pages 112 through 116 (fascinating book with a nmber of incidents described by operators early in the war in Missouri) See it on Google books. http://books.google.com/books?id=trpBAAAAIAAJ&printsec=frontcover&dq=The+Military+Telegraph+During+the+Civil+War+in+the+United+States&source=bl&ots=vlY4FsWyzx&sig=poqhY6LRQs7oyNG03ojnkYAyAmU&hl=en&ei=Ur6RS8m7C4f4NcKT4JsN&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAcQ6AEwAA#v=onepage&q=rolla&f=false
This site discusses the evolution of the Springfiled Rolla St. Louis Wire/Telegraph roads through Webster county. It sheds light on what was where when... http://www.chrisanddavid.com/caddo/index.shtml
The best info on the August/Sept 1861 date is this entry:
“Telegraph to Rolla: We see it stated in the St. Louis
papers that a line of telegraph is to be extended to this
place for military purposes. This will be another lift to our
young and thriving little city, placing us in immediate connection
with the rest of the world.” (Rolla Express, June
17, 1861, p. 2)
See http://library.mst.edu/documents/dataminerfall04.pdf
Several Greene Co. History sites state the first telegraph line came from Jeff City via Rolla on the old wire road to Fort Smith Arkansas in 1860. This matches the discussion about Wire Road #1 in Webster County. Thus it appears that a commercial telegraph line may have reached Rolla in 1860 from Jeff City but clearly was replaced in the fall of 1861 by a wire from St. Louis ordered by Fremont and clearly under the control of the military. W. H. Parsons was the first operator in Springfield.
Though not part of the discussion I stumbled on this little tidbit re destruction of the line in 1864 twice no less by the same lady. (copy and past into a browser its a long entry...)
http://cdm.sos.mo.gov/cdm4/results.php?CISORESTMP=results.php&CISOVIEWTMP=item_viewer.php&CISOMODE=grid&CISOGRID=thumbnail,A,1;title,A,1;subjea,A,0;descri,200,0;none,A,0;20;title,none,none,none,none&CISOBIB=identi,A,1,N;title,A,0,N;creato,200,0,N;none,A,0,N;none,A,0,N;20;identi,none,none,none,none&CISOTHUMB=20%20(4x5);identi,none,none,none,none&CISOTITLE=20;identi,none,none,none,none&CISOHIERA=20;title,identi,none,none,none&CISOSUPPRESS=1&CISOTYPE=link&CISOOP1=exact&CISOFIELD1=relati&CISOBOX1=Sarah+Jane+Smith+Papers%2C+1864-1865&CISOOP2=exact&CISOFIELD2=title&CISOBOX2=&CISOOP3=exact&CISOFIELD3=creato&CISOBOX3=&CISOOP4=exact&CISOFIELD4=CISOSEARCHALL&CISOBOX4=&c=exact&CISOROOT=%2Fmack
FWIW
John R