When an attorney who declines to take your case tells you to seek legal advice "immediately" it is the attorney's way of letting you know that all claims are subject to a statute of limitations, or a deadline for filing. The attorney is encouraging you to hire an attorney as soon as possible to protect your legal rights, whatever they may be.
(1) The attorney does not want your case: could be its a losing case; could be it would not be profitable for the attorney to spend limited time and resources with little ROI; could be its outside the attorney's skill sets; could be the attorney does not believe he/she can work with YOU---there are scores of reasons, you'll never know why if they don't tell you directly. Ask them. I always tell my prospective clients why I won't take their case--it 'isn’t always pretty, but it’s the best thing for the client.
(2) By telling you to immediately seek counsel, the attorney has done his/her duty insofar as telling you that you MAY have statute of limitations or short windows in which your claim/suit can be filed. Also, evidence begins to fade over time, witnesses’ waiver and mix memories with things they did not actually witness, paperwork gets lost, people move away--passage of time is sometimes the enemy of a litigant.
NOT LEGAL ADVICE. FOR EDUCATION AND INFORMATION ONLY. Mr. Rafter is licensed to practice in the Commonwealth of Virginia and the US Federal Courts in Virginia. There is no implied or actual attorney-client relationship arising from this education exchange. You should speak with an attorney licensed in your state, to whom you have provided all the facts before you take steps that may impact your legal rights. Mr. Rafter is under no obligation to answer subsequent emails or phone calls related to this matter.
Your question indicates that "several attorneys" have told you to seek other representation "immediately," but that none of them have explained why they won't take your case. If by several attorneys you mean multiple unaffiliated attorneys from separate firms, I find it surprising that not one of them has explained their decision to decline your case. They may not have the obligation to explain, but in my experience, most conscientious lawyers will provide some reason for refusing to represent a potential client.
I'm more troubled by their warning to seek counsel immediately. You don't explicitly indicate that these lawyers failed to explain their reason for the warning , but your question about what is legally meant by the term "immediately" implies that they didn't. I agree with the other contributors here that the warning to act immediately probably means that a statute of limitation or repose may be about to run (though I can imagine other reasons for immediacy, depending upon the type of case you're attempting to pursue.) But I don't agree that a mere cryptic warning to immediately obtain other counsel, unaccompanied by any additional explanation as to the nature of the threatened harm or or the date on which that harm might occur, will necessarily satisfy the attorney's ethical responsibility. Under certain circumstances, an attorney-client relationship can arise for a limited purpose, even if a broader representation has been declined. By failing to be specific about when and to what extent potential claims might become time-barred, an attorney can cause prejudice to the client and may well be accused of having breached his or her ethical obligations.
Because your question doesn't recite enough background for us to definitively know either what the lawyers in question were thinking or whether they actually were required to do more than they did to protect your interests, It would be presumptuous for me to imply that they violated any ethical rules. Moreover, I'm not licensed in PA and am unfamiliar with your state's disciplinary rules. But clearly, considerations of good practice and common courtesy should have compelled them to send you off with a clearer understanding of your situation. In any event, I agree that you should understand their use of the word "immediately" to mean "today, or as soon thereafter as possible."