Regular Expression works in form correctly but for string from excel not

Question

I have a form that validates string with this:

    [RegularExpression(@"[a-zA-Z]+[a-zA-Z\d_]*[a-zA-Z\d]")]
    [MinLength(5)]
    [Required]
    public string JoinLink { get; set; }

this statement accepts anything that start with alphabetic and after that _ or digit or word and the end just word and digit. example:

asdfg123    //match
123546asdfa //not match
asdf1235_   //not match
https://telegram.me/agdfgkjafdg16456 // not match

in other hand when user upload excel file i have to check that content is correct.like this:

  string reg = @"^[a-zA-Z]+[a-zA-Z\d_]*[a-zA-Z\d]";
  for (int i = 0; i < ds.Tables[0].Rows.Count; i++)
  {
  string link = ds.Tables[0].Rows[i][0].ToString();
  bool result = Regex.IsMatch(link, reg);

  if (result)
  {
   //Do somthing 
  }

Everything is ok until a string is https://telegram.me/... or any address. why result for addresses is true?

Can you help me ?

Thanks in advance