Do the feelings related to Transference always originate from parents? As I understand, 


  Transference is a phenomenon which is related to human behavior where humans unconsciously redirect/transfer their feelings about a subject in the past to apply it to a subject in the present.


Is this definition correct?

Does the subject in the past always have to be Parents? What did Freud say about this?
Short answer
Transference is often related to feelings felt toward parents, but not always.

Background
Transference (Hughes &amp; Kerr, 2000) is 


  the phenomenon whereby we unconsciously transfer feelings and
  attitudes from a person or situation in the past on to a person or
  situation in the present. The process is at least partly inappropriate
  to the present 


According to (Ladson et al., 2007), transference are


  unconscious feelings that are transposed onto another significant individual. 


These feelings can be beneficial for therapeutic purposes, but intense, sexualized transference can be disadvantageous. Sexualized transference is 


  any transference in which the patient's fantasies about the analyst
  contain elements that are primarily reverential, romantic, intimate,
  sensual, or sexual.


The authors give an example of projections of sexual feelings experienced during early childhood relationships. 

So although transference per se is often described in relation to parental feelings of submission, vulnerability and openness in a relation between therapist and client, transference can take other shapes. 

References
- Hughes &amp; Kerr, Advances in Psychiatric Treatment (2000); 6(1) 57-64
- Ladson et al., Psychiatry (Edgmont) (2007); 4(3): 47–50